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Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
CHAPTER 3 SOUND. ULTRASOUND DIAGNOSIS
3.1. Mechanical waves and sound. Physical parameters of sound: frequency, intensity, speed
of propagation, sound pressure. Sound resistance. Reflection, refraction and absorption of sound.
Extracorporeal lithotripsy
At rest, the constituent particles of the solid and liquid bodies are located in equilibrium position
due to the equality of all forces acting between them. The same is valid for each micro volume in the
space filled with gas. When a particle is displaced from its equilibrium position by an external driving
force a reaction counter force arises. When the external force is removed, the counter force compels the
particle to vibrate freely around its equilibrium position with a frequency called natural frequency, o.
This is a free, elastic vibration of the particle around its equilibrium position. As the free vibration is not
supported by external energy (force), it usually attenuates due to the friction between the vibrating particle
and environment. The amplitude of free vibration usually declines exponentially over time. The vibrations
of the displaced particle can also be forced, when the vibration amplitude is maintained constant by a
periodically acting external driving force. The forced vibration is performed at a frequency equal to the
frequency of the driving force. The amplitude of the forced vibrations depends on the proximity of the
frequency, , of the driving force to the natural frequency, o, of the vibrating particle. When  approaches
o,
the
amplitude
of
vibrations steadily increases,
this
event
is
called
mechanical
(acoustic)
resonance.
Fig. 3. 1. 1. (Above)
Compression
and
rarefaction of the particles
of a medium at longitudinal
mechanical wave. (Bellow)
Displacement
of
the
constituent particles from
their equilibrium positions
on the axis of propagation
of a mechanical wave.
Mechanical
waves
arise in material media (solids, liquids, gas) when a constituent particle (or gas microvolume) is displaced
from its equilibrium position. The particle starts to vibrate around its equilibrium position with a certain
frequency and amplitude. Due to the elastic forcies of interaction between the constituent partices this
vibration is transmitted, with a little delay, from a group of particles to the next group of particles
producing zones of compression and rarefaction (Fig. 3.1.1). Once it arises at a given place the mechanical
wave propagates through the medium with a certain velocity. The mechanical wave is actually an elastic
vibration of the particles of medium in the form of adjucent zones of compression and rarefaction.
Thereby, the particles do not move along the axis of wave propagation, they only vibrate around their
equilibrium positions in a sine way. What is actually moving through the medium are the compression and
rarefaction zones, accompanied by a transfer of mechanical energy.
In physics the sound represents forced vibration in an elastic medium, i.e., local elastic
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
deformation of the medium, a mechanical wave. In a particular sense sound is a mechanical wave which
propagaties in air and can be detected by the human ear. Such sound (acoustic) wave, however, can occur
and spread in other material media (solids, liquids, gas) as well, but not in vacuum. Based on the way the
particles vibrate relative to the axis of wave propagation the mechanical waves, including the sound
waves, are divided into transverse and longitudinal waves. Mechanical waves in the gaseous medium are
always longitudinal, while those in liquid and solid media can be of both types - longitudinal and
transverse ones.
Fig. 3.1.1 shows the displacement, A, of the particle from its equilibrium position as a function of
the distance. Similar form has the time dependence of the displacement of the vibrating particle from its
equilibrium position. This time dependence has harmonic character and it is described by a sine wave: A =
Ao.sin (.t+), where Ao is the maximal displacement (the amplitude of vibration), (.t + ) is the phase
of vibration,  is the angular frequency of vibration, and  is the initial angle of vibration, the phase
angle. The time spent by the particle to return back to its starting position is the period of vibration, T. The
frequency of vibration,  = 1/Т = /2 is the number of vibrations per second. Wavelength  is the
smallest distance between two particles vibrating synchronously (in phase). For one period of time, T, the
wave travels a distance of one wave length, , therefore the speed of wave propagation, C, is given by the
formula C = /T. The number of wavelengths which cover a distance 2 meters (about 6.28 m) is named
wave number k = 2 / .
The source of mechanical wave dictates the frequency, , and amplitude, Ao, of forced vibrations
of particles. In turn, the medium determines the speed of wave propagation, the attenuation rate, and the
nature of vibration (transversal or longitudinal) relative to the axis of the wave propagation.
In condensed media (solids, liquids, tissues) the mechanical waves travel at a much higher speed
and attenuate much lower than in air, due to the stronger interactions between their constituent particles.
The sound speed in air (20°C) is about 340 m/s, while in water and in human tissues the sound propagates
with a substantially higher speed of about 1500 m/s, in steel with 5000 m/s, and in glass with 5400 m/s.
The propagation of transverse waves in a solid media and in human tissues is accompanied by
elastic shear deformation. In this case the velocity of transverse sound waves is given by the formula C =
(G/)½, where G is the elasticity modulus of shear strain, and ρ is the density of the medium. The
longitudinal mechanical waves are accompanied by deformation of the type extending – contraction and
its velocity is given by another expression, C = (Е/)½, where E is the elasticity modulus of extention
(Young's modulus). For all solids E > G, so the longitudinal waves propagate faster than the transverse
ones. This deteriorates the image at the ultrasound diagnosis of internal organs.
According to Fig. 3.1.1 the propagation of a sound wave is accompanied by a formation of areas
where the particles are in the lowest position, called depressions of the wave. The areas in which the
particles are in the highest position are called the crests of the wave. The place at which the wave has
arrived at a certain moment is called wave front. Based on the shape of the wave front the sound waves are
designated as flat, spherical, cylindric and others. The speed at which the front of sound wave spreads is
called phase velocity.
Wave that moves away from its source is called a traveling wave. If a traveling wave reaches a
barrier, which is perpendicular to the axis of propagation, the wave is reflected and comes back following
the same axis. The reflected wave moves at the same speed and frequency as the incident wave but its
phase could be changed giving rise to complex interference of both waves. There are cases when the
incident and reflected waves fully overlap and form the so called standing wave. In a medium with
standing wave there are always places where the particles do not vibrate; these places are called nodes of
the standing wave. The places, called antinodes, are occupied by particles that are displaced at the
maximal distance from their equilibrium position. The distance between two adjacent nodes (antinodes) is
λ/2. The standing wave does not transfer mechanical energy as the incident and reflected waves both carry
equal energies in opposite directions.
Depending on the frequency of vibration, , the mechanical waves are referred to as infrasound (
less than 16 Hz), sound ( from 16 Hz to 20 kHz) and ultrasound ( higher than 20 kHz to several MHz
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
typically). The human ear is sensitive only to mechanical waves with a frequency between 16 Hz and 20
kHz (auditory range). Other species are, however, sensitive to different auditory intervals of frequency
(Table 3.1.1). In ordinary sense, sound represents a mechanical wave that traveles through air with a
frequency of 16 Hz to 20 kHz.
If the sound source and the sound
detector are immobile (stationary) relative
Table 3. 1. 1. Approximate hearing ranges of
to each ather, the frequency of the received
various species.
sound is equal to that of the emitted sound.
If the sound source or the sound detector
Species
Low Frequency
High Frequency
or both move relative to one another, the
Limit (Hz)
Limit (Hz)
frequency of the received sound, , is
Beluga whale
1,000
120,000
different from the frequency of the emitted
Bat
2,000
110,000
sound o. This phenomenon is called
Bullfrog
100
3,000
Doppler effect, named after the Austrian
Cat
45
64,000
physicist Doppler. For example, if the
Catfish
50
4,000
sound source and the detector move along
Chicken
125
2000
the straight line joining them with the
Cow
25
35,000
speeds V1 and V2, respectively, then  =
Dog
65
45,000
o.(C – V2)/(C - V1). The Doppler effect is
used in ultrasound imaging of the moving
Elephant
16
12,000
internal organs.
Horse
55
33,000
Human
16
20,000
Passing through an area, S, the
Owl
125
12,000
mechanical wave brings acoustic energy,
E. It equals the sum of the energy of
elastic deformation of the medium plus the kinetic energy of vibrating particles. The acoustic energy, E,
transferred perpendicularly through a unit area, S, per unit time, t, is called intensity, I, of the mechanical
wave, i.e., I = E/(S.t) (W/m2). It depends on the density of the medium, , the amplitude of vibration, A,
the speed of sound propagation, C, and the frequency of vibration, : I = 22 . A2 . 2 . С. This formule
demonstrates that ultrasound, even having small amplitude of vibrations, possesses high intensity because
the vibration frequency is very high! The high concentration of energy in the ultrasound wave could
produce various and strong effects, which are widely used in engineering and medicine.
When a sound wave propagates in air, the gas molecules periodically are brought closer and
drawn apart. In phase with these changes in gas dencity the gas pressure also fluctuates around its
equilibrium value, equal to the atmospheric pressure. These periodic changes of the gas pressure are
referred to as sound pressure, Ps. The higher the amplitude of the sound pressure, Ps, the higher will be the
intensity, I, of sound wave, because I = 0,5.Ps2 / (.C). Similar formula is also valid for liquid media. The
product .C = Z is referred to as sound resistance (acoustic impedance) of the medium.
In general, the acoustic impedance Z is the ratio of the acoustic pressure, p, to the acoustic
volume flow, W, through a unit area. Specific acoustic impedance z is the ratio of the acoustic pressure
p, to the acoustic velocity of the vibrating particles. When the mechanical wave is transmitted through
a narrow and long pipe (e.g., the trachea of lungs), the acoustic impedance, Z, is expressed by the
formula Z = P/W, wherein P is a sound pressure, and W is the volume flow of the vibrating medium
through the pipe.
The acoustic impedance, Z, is dependent only on the properties of the sound medium. For media
with greater Z, the sound pressure should be greater in order to transmit a certain amount of acoustic
energy. In addition, Z determines the energy losses of sound wave during its reflection and refraction at
the boundary of two media with different acoustic properties. When a mechanical wave with intensity, Io,
arrives at the boundary between two media with different sound resistances, Z1 and Z2, it is partially
reflected and partially refracted. The reflectance depends on the difference in acoustic resistances by the
following formula: Ir / Io = (Z2 – Z1)2/(Z2 + Z1)2, where Ir is the intensity of the reflected sound wave. The
greater the difference in acoustic impedances, the greater part of the sound energy will be reflected, and
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
the lower portion of it will enter the second medium. For example, let the sound wave moves in air and
reaches a water surface. The Z of the aqueous medium is 3500 times higher than that of the air, hence,
only 0.12% of incident sound energy will penetrate into the water medium. Such a case will be valid at the
boundary between the middle part and inner part of human ear provided there were no ossicles (auditory
bones).
When a mechanical wave reaches some obstacle (barrier, wall, massive body) similar reflection
and refraction also occur. However, if the dimensions of the obstacle are close to or less than the sound
wave length another type of phenomena occurs, diffraction (wave surrounds the barrier). For example,
infrasounds and low frequency sounds having  about several decimeters and meters, bypass obstructions
with such dimensions and can not be used for diagnostics of the internal organs of a human.
Mechanical waves are used for noninvasive in vivo breaking of solid kidney and gall stones into
small pieces which are later removed through the urinary tract. The method is known as extracorporeal
lithotripsy. The concretions (stones), however, must have appropriate mechanical properties and
dimentions. This method causes breaking apart of oxalate concrements, which have a high embrittlment,
and not of phosphate ones, which are elastic.
Fig. 3. 1. 2. Scheme of extracorporeal shock wave lithotripter (left). In order to avoid the
damage of the soft tissue around the kidney stone, the rays of the mechanical wave are concentrated
in the stone from all directions (right).
For this purpose, the patient is placed in a water-filled vessel to avoid unwanted reflections of the
waves during their passage through the patient’skin. The vessel has an elliptical cross-section with two
focuses, F1 and F2 (Fig. 3.1.2). From the geometry it is known that every ray emanating from the first
focus of the ellipse, after its reflection, necessarily arrives at the second focus. Initially the stone is
precisely localized by ultrasonography and the patient is positioned in order the stone to be placed right in
the second focus F2. The mechanical waves are produced by an electric discharge between two electrodes,
located at the focus F1. After the rays are reflected from the walls of the ellipsoid they focus at F2. Each
separate ray has a subcritical intensity and, even at full absorption of its energy, it could not damage the
soft tissues through which it passes. In fact, soft tissues have low acoustic impedance and absorb a little
portion of the acoustic energy. All the reflected rays, however, concentrate at F2 and their acoustic energy
is absorbed chiefly by the gall or kidney stone. As a final result, the stone is destroyed and subsequently
removed through the urinary tract.
Except the above mentioned, another dry ultrasound lithotripsy with a low frequency (40 kHz) is
applied recently. The gallstone or kidney stone of the patient is precisely localized by ultrasonography or
fluorography. Ultrasound generator is positioned close to the patient body and directs a narrow, high
intensity ultrasound beam to the concrement. Usually the concrement is broken apart by a single impact of
the beam.
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
3.2. Psycho-physical characteristics of sound: pitch, loudness and timbre. Threshold of
audibility and level of intensity. Law of Weber-Fechner. Audiometry. Methods of sound insulation.
Sound diagnostics methods
Acoustics (from Greek akustikos - hearing) is a branch of physics, which studies the elastic
vibrations and waves propagating in the mechanical media, in particular the sound waves that cause
auditory sensations in human.
According to the type of vibration the sounds are divided into tones, noise and sound shocks
(strikes). Noise and sound shocks are prolonged and short non-periodic vibrations, respectively. Tones,
also called musical sounds, are periodic vibrations. We distinguish pure (simple) and complex tones. The
tone is pure, if the vibration has sine wave (harmonic) character. This sound can be produced by a tuning
fork and sound generator. Complex tones are periodic vibrations with significantly more complex
character, which are repeated over time. They are produced by the human voice and musical instruments
and convey the essencial body of information to the human ear.
According to the theorem of Fourier each complex tone can be represented as a sum of simple
sinusoidal vibrations of different amplitudies and frequencies. The vibration having the lowest frequency
(о) is called a fundamental tone, while vibrations having higher frequencies are termed overtones. Those
overtones that have frequencies multiples of the frequency of the fundamental tone, i.e., frequencies equal
to 2о, 3о etc., are called harmonics or partials. Musical instruments produce only such musical tones
which contain a fundamental tone and its harmonics.
Fig. 3.2.1. Left: sound spectrum of a pure tone with the frequency of 440 Hz. Right: sound
spectrum of musical tone with the fundamental frequency of о = 880 Hz and its 7 harmonics.
Musics uses a number of pure tones arranged in groups called octaves. Each octave contains
seven pure tones which, ordered by increasing their frequencies, are referred to as Do (C), Re (D), Mi
(E), Fa (F), Sol (G), La (A) and Si (B). The seven tones of the first octave are called basic tones. Their
first harmonics constitute the next second octave, their second harmonics - third octave, etc. For
example, the pure tone La (A) of the first octave has the frequency of 440 Hz, and the same tones of
the second and third octaves have the frequencies 2 × 440 Hz and 3 x 440 Hz, respectively.
The combination of the fundamental tone and its overtones constitutes the so called acoustic
spectrum of the complex tone (Fig.3.2.1). Individual sound sources, such as various musical instruments
and human voices can produce complex tones with the same basic tone and with different acoustic
spectrums (Fig.3.2.2). The human ear has the ability to distinguish the complex tones that have the same
fundamental tone and different acoustic spectrums. The different auditory perceptions based on the
acoustic spectrum of different complex tones having the same fundamental tone is designated as timbre
(color) of complex tones. So the timbre of the complex tone depends on the whole spectrum of overtones,
mostly on the low overtones because they have larger amplitudes. Meanwhile, overtones of highest
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
frequencies impart freshness and beauty to the musical tone.
Frequency , intensity, I, and acoustic spectrum are the basic physical (acoustical) parameters of
sound waves. In turn, the human ear converts these physical parameters in respective neuro-psychic
characteristics of sound (pitch, loudness and timbre) which all convey information to human.
The pitch of sound depends mainly on the frequency, , of vibration of the particles (frequency of
the sound wave, or the number of waves that pass through the ear per unit time). The higher the , the
higher is the sound pitch. Receiving different complex
tones, human distinguishes them by their pitch which
corresponds to their fundamental frequencies, o.
Frequency resolution of the ear is determined by the
smallest difference in the frequencies of two pure
tones that are perceived as having different pitchs
(usually 3 Hz).
Figure 3.2.2. Line spectra of three musical
instruments playing a tone with the same pitch and
loudness.
Loudness (volume) of the sound depends
on the maximal displacement (amplitude of the
vibration) of the particles, i.e., how far the oscillating
particles are displaced from their equilibrium position.
The sounds are louder when the intensity (energy
density) of their sound waves is larger, i.e., the sound pressure is greater. Thus, sounds with the same
frequency, , that have different intensity, I, are perceived as having different loudness, F.
In some cases, the pitch of a sound depends, albeit slightly, and on the sound intencity
(volume); the greater the intencity, the higher would appear the sound pitch. However, this effect is
much weaker compared to the main dependence of sound pitch on sound frequency.
When the sound weakens, a minimal intensity, Imin, is reached whereat the sound is no longer
heard. Imin is the threshold of hearing. The threshold of hearing determines the sharpness of hearing
(auditory acuity) of different individuals. The lower the Imin, the greater is the sharpness of the hearing.
The threshold of hearing is different at various sound frequencies. Determination of Imin as a function of
frequency is called audiometry, which gives a quantitative presentation of the status of the patient ear. The
hearing acuity is greatest at about 0.6 - 2 kHz, and this lowest threshold of hearing is called standard
threshold of hearing. It is generally accepted that for a healthy individual the standard threshold of
hearing, Io, lies at 1 kHz and has a magnitude of 2.10-5 N /m2.
The loudness, F, and the intensity, I, of the sound are related according to the general
psychophysical law of Weber-Fechner: if the irritating physical factor (the sound intensity, I) increases in
geometric progression, the aroused feeling (loudness, F) increases in arithmetic progression. This can be
expressed by the formula F = K.lg (I/Io). Here Io is the standard threshold of hearing, measured at 1 kHz
and the variable lg (I/Io) = E is called sound intensity level. The coefficient K is, however, frequency
dependent. It is accepted that K = 1 at 1 kHz, while at low and high frequencies K decreases.
The measurement unit for loudness is phone. The sound intensity level, E, is measured in the units
bel (B), however, a ten-fold smaller quantity, decibel (dB), is frequently used, i.e., E (bel) = 10E (decibel).
Although loudness, F, is proportional to the intensity level, E, both variables are expressed in different
measurement units. Loudness is represented by phones, while the intensity level in bels (or decibels). Only
at the frequency of 1 kHz, 1 phone = 1 B.
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
Fig. 3.2.3 (left) shows the frequency dependence of the so called isophonic curves corresponding
to sounds with different frequenies and the same loudness. Each curve shows how the intensity level at a
given frequency should be adjusted in order to give the desired sensation of loudness. At the same figure
the threshold of hearing is shown as a function of frequency. When the intensity level, E, is too high
(about 120 dB) a pain sensation results; this intensity level is the pain threshold. The area of hearing
(auditory space) is placed between the hearing threshold and pain threshold curves (Fig. 3.2.3 - right). At
each frequency the intensity difference between the hearing threshold and the threshold of pain is referred
to as a dynamic range. For normal hearing the dynamic range has the maximal value of 120 dB at about 1
kHz. Within the auditory space four areas of speech audibility are distinguishable; an area of quiet
hearing of speech without understanding (speech awareness, speech detection), area of intelligible
speech (speech intelligibility, speech recognition, speech reception), area of pleasant
loudness and area of unpleasant perception of speach. Amplitude resolution of the ear is its ability to
distinguish between two sounds of different intensities (about 3 dB in norm).
Fig. 3. 2. 3. Frequency dependence of the intensity level for the same loudness sensation
(left). Area of hearing (right).
Fig. 3.2.3 (left) shows the frequency dependence of the auditory sensitivity for normal ear. For
low-intensity sounds the sensitivity is highest at 1 kHz while for high intensity sounds the sensitivity at 1
kHz is the lowest. This means that at 1 kHz we have greater acuity of hearing weak sounds and strong
protection against hearing loud sounds. This is because the human ear is adapted to hear primarily sounds
with frequencies about 1 kHz, evolutionary evolving the ability to amplificate the weak sounds and to
suppress loud sounds about this freqiency. Responsible for these special properties of ear are mainly the
ear bones. The ability to hear intelligible speech is best at such sound intensities whose isophone curves
do not depend on frequency providing minimal frequency distortions.
Noise and sound strikes produce harmful effects on humans, especially at larger durations and
intensity levels (70 dB and greater). Above 80 dB (as in discotheques), they cause permanent hearing and
psychic disabilities. This type of sounds are able to weaken the hearing sensitivity and can cause partial or
total loss of hearing. The rhythms of heart beats and breathing both can be permanently disrupted. Noise
acts on the nervous system, causing fatigue, decreased performance and various nervous disorders. Most
damaging is the noise having a frequency of 1-2 kHz, where the severity of hearing loss is greatest.
In many cases noise protection is required. It is chiefly based on reducing the intensity of sounds
using the following methods:
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
1) Sound intensity, I, decreases as 1/ r2 against the distance, r, to the sound source. Accordingly,
the source is distanced away to obtain a safe intensity level.
2) When passing through a given medium, the sound is absorbed and damped. The sound intensity
decreases exponentially depending on the thickness of the absorbing layer. Therefore, a proper layer
(screen, wall, tree and planting strip, line of trees) with appropriate thickness should be used in order to
suppress noise. Most screens are usually made up of a material containing pores, air bubbles that reflect
and absorb sound waves.
3) The sound, having an avrage wavelength, m, is made to pass through a wall containing two
parallel plates with an air volume between them. The two plates are spaced at a distance, d = 0.5 m and,
hence, the sound waves reflected by the second plate have a phase difference of 180° compared to that of
incident waves. Comming back the reflected wave quenches the incident one and the sound become
reduced.
To control the noise level in workplaces, streets, airports ect, special noisemeters are used,
consisting of a microphone, electronic amplifier and a set of electronic frequency filters. These
noisemeters analyze the frequency and amplitude distributions of the noise and compare them with the
acceptable hygiene standards.
Ausculation is a classical method for sound diagnosis of heart sounds, breath sounds and the
sounds produced in gastrointestinal tract. The doctor uses sound tube (stethoscope) or resonator box
(fonendoscope) which gather the natural sounds emitted by a tested organ (lung, heart, stomach) or the
sounds of the fetus, amplifies them and conducts them to the doctor’ears. Recently, the continuous Dopler
sonography is used to monitor the movements of heart valves and blood.
The percussion is another method for sound diagnosis of thorax and abdomen whereat the
doctor uses a mallet or his finger to apply a leisurely blow on the indicated surface. With a headset the
doctor hears the generated sounds and follows their attenuation and echos. The sounds could be resonant
(drum-like) or dull. The former indicates air-containing voids and the latter evidences for solid material in
the underlying tissues.
With the two methods the doctor analysises the sound volume, timbre, and damping rate which all
convey information about the status of some internal tissues and organs.
In phonocardiography the sound is captured by a microphone and converted into electric
impulses, which are amplified by an electronic amplifier and recorded on paper. In healthy adults the
recorded sounds are devided into two groups, T1 and T2. The first group (T1) is recorded at the time when
the left ventricle of the heart contracts, and the second (T2) during the closure of aortic valve. Additional
two groups of noises (T3 and T4) are registered with children. Using phonocardiograph noises arising in
various blood vessels could also be registered. The source of such noise is the occurrence of turbulence in
blood flow at each local constriction, for example, at a place of external compression or accumulation of
internal plaque or at local extension (aneurysm) of the blood vessel.
3.3. Physical mechanisms underlying the hearing apparatus in human. Determining the
location of the sound source. Auditory prosthesis and implant
Ear transforms the mechanical energy of sound waves into nerve impulses, allowing the extraction
of information based on the physical parameters of sound - frequency, intensity, spectrum and the
direction of propagation. It represents a perfect sensory organ capable to percept vibrations in a wide
range of frequencies and amplitudes.
Human ear consists of three parts, indicated as external, middle and inner ear (Fig.3.3.1). The
outer ear is a pipe whose inlet, the auricle, is shaped like a funnel and its oulet is closed by a vibrating
membrane. The middle ear contains the auditory bones that concurs the different acoustic resistances of
air and water. The most important part is the inner ear, which contains the receptor cells located in the
cochlear apparatus. The role of the outer and middle ears is to collect and amplify the mechanical
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
vibrations and to convey them to the receptor cells, which in thurn convert the vibrations into nerve
impulses. It is very important to notice that receptor cells are positioned in an aqueous medium while the
outer and the middle ears are hollow and air-filled. Therefore, the inner ear has a much higher acoustic
impedance than that of the outer and middle ears. This requires additional elements - auditory bones to
conform different sound resistances of the three parts of the ear.
Sounds that arrive at human ear represent a longitudinal mechanical wave propagating in the air.
The auricle acts as a funnel collecting and amplifying the sound wave about 3 times irrespective of its
frequency and amplitude. Then the sound wave enters the ear canal, where it is amplified by resonance. At
the end of the ear canal sound wave meets the tympanic membrane (ear drum) and compel it to vibrate.
Further, the ear drum vibrations are transmitted to a lever system consisting of three little bones (ossicles),
called hammer (malleus), anvil (incus) and stirrup (stapedius), located in the middle ear. As the last ossicle
is connected with the oval window of the inner ear the vibrations finally reach the fluid in the inner ear.
Fig. 3. 3. 1. Cross-section of
a human ear.
The external auditory canal
of the ear performs the role of an
acoustic resonator with a resonance
frequency of 2 - 3 kHz. Its length (2.3
cm) is about 0.25 part of the length of
the sound wave at this frequency and,
therefore, the wave that is reflected
from the eardrum coincides by phase
with the coming wave. Thus, while
the auricle enhances all vibrations
regardless of their frequencies the auditory channel only amplifies the vibrations of a certain frequency
(resonance).
The pressure difference on both sides of the tympanic membrane must be close to zero in order to
avoid the puncture of tympanic membrane. The Eustachian tube, which connects the middle ear to the
atmosphere, prevents this pressure drop to reach dangerous values at diving, loud noise, etc.
Physically speaking, the lever system of auditory bones performs three important tasks as
illustrated in (Fig. 3.3.2):
1. It coordinates the sound impedances of both the middle and inner ears lowering the threshold of
hearing. The acoustic impedance of the water in the inner ear is about 3500 times greater than that of the
air in the middle ear. If there were no auditory bones, only 0.014 % of the sound energy arriving at the
middle ear would be absorbed in the inner ear. The remaining 99.986% part would be reflected back
without any effect.
2. The auditory bone system enhances the sound pressure applied on the oval window
about 20 times compared to that exerted on the eardrum. This is because the area of the oval window is 20
times smaller compared to the area of eardrum. This additionally increases the hearing acuity.
3. Sounds with high intencities impose too strong vibrations on the eardrum which should be
dangerous for the oval window. In this case, however, the first auditory bone, hammer, transforms the
predominantly longitudinal vibrations of the eardrum into predominantly transversal ones. This
mechanism prevents the overcritical vibration of the oval window, protects it from damage and reduces
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
the pain threshold.
Fig.
3. 3. 2.
Schematic
diagram of
human ear.
The inner ear contains spiral-shaped cochlea which has 2 and ¾ turns. Along the axis of the
cochlea tube the so called middle chamber is positioned, filled with a fluid (perilymph) and immersed into
another aqueous medium with different composition (endolymph). The bottom wall of the middle
chamber is called basilar membrane and the upper wall is termed tectoreal membrane. The latter is
covered with about 10,000 auditory (receptor, hair) cells. In mammals these cells are of two types, called
inner and outer hair cells (Fig. 3.3.3). When a sound wave arrives at the oval window of the inner ear, the
vibrations are immediately transmitted to the proximal end of basilar membrane. Next the vibrations start
to propagate along the axis of basilar membrane in the form of a traveling wave. The outer hair cells take
up the vibrations of basilar membrane, enforce their amplitude by 60 dB and transmit them to the tectoreal
membrane. The inner hair cells absorb the intensified oscillations of the tectoreal membrane and transform
them into nerve impulses which reach the brain via the auditory nerve.
The sound, perceived by ear, is louder when its amplitude of vibration is larger. The louder sound
causes the hairs of the irritated receptor cells to vibrate with greater amplitude, thus generating a larger
number of nerve impulses per unit of time. This allows the ear to discriminate sounds with different
amplitudes transforming the amplitude into nerve impulses with different frequencies.
The ability of ear to distinguish sounds with different frequencies is explained by the so called
"spatial theory". According to this theory the low frequency oscillations irritate the receptor cells located
on the distal end of the basilar membrane, while high frequency oscillations irritate cells on the initial
portion of the basilar membrane, proximal to the oval window. There are four mechanisms by means of
which the traveling waves, depending on their frequency, irritate different auditory cells located at
different places along the basilar membrane.
1. With a total length of about 32 mm, the basilar membrane gradually changes its mechanical
properties, density and thickness from its beginning to its end. Near the oval window it is highly dense and
hard and has a thickness of 0.5 mm. At its distal end the membrane becomes highly deformable and
elastic, and reduces its density and thickness to about 0.1 mm. These mechanical properties facilitate the
absorption of low-frequency sounds at the apical end and high-frequency sounds at the basal end, i.e.,
different parts of the basilar membrane resonate at different frequencies.
2. The traveling wave reaches as greater distances on the basilar membrane as lower is its
frequency. The reason for this limitation is the water medium of the inner ear which strongly inhibits
(quenchs, attenuates) the oscillations of basilar membrane. The higher the vibration frequency the shorter
is the traveling path of the running wave (Fig. 3.3.3). For example, a vibration with frequency of 100 Hz
manages to reach the far, apical end of membrane while oscillation with frequency of 20 kHz fades away
at the basal end of membrane. At the end of its traveling path the vibration dramatically increases its
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
amplitude and abruptly attenuates losing fully its mechanical energy. Therefore, all the energy of the
traveling wave concentrates at the final step of its traveling path and the local auditory cells are subjected
to the strongest irritation.
Fig. 3.3.3. Above: schematic diagram of the receptor apparatus of the ear. Bottom: a form of
the traveling wave at different frequencies: ν1 <ν2 <ν3.
3. The final, strongest oscillations of the traveling wave are additionally enhanced by the local
outer hair cells. As a rule, the vibrations of basilar membrane bent the hairs of outer hair cells and this
mechanical irritation induces the depolarization of their membranes. Depolarization of the outer receptor
cells compel them to elongate and shorten in phase with the sound vibrations (electro-mechanical
conversion). This causes the local part of tectoreal membrane to vibrate with much larger amplitude than
that of basilar membrane (electro-mechanical amplification of the vibration). In turn, the oscillations of
the tectoreal membrane irritate the inner receptor cells leading to their depolarization. The depolarization
of inner auditory cells compels them to release neurotransmitters, which are caught by the nearby nerve
cells which respond with the generation of nerve impulses. Using the auditory nerve axon these nerve
impulses reach the appropriate point in the hearing center of the brain and cause a sense of sound with the
corresponding pitch.
4. The outer hair cells of mammals have the same thickness of about 7 μm, but different length,
which depends on their position on the basilar membrane (Fig. 3.3.4). The different length of these cells
also affects their sensitivity to the oscillations with different frequencies as longer cells could resonate to
low-frequency vibrations and shorter ones could take up more readily the high-frequency vibrations.
Thus, the information about the sound pitch is derived based on the place of basilar membrane
where the running wave damps down irritating the local hair cells. The same mechanism is responcible
and for the perception of sound timbre as the latter is due to the large number of overtones (pure
vibrations) incorporated in the complex tone.
Latest research indicates that an important part of the receptor potential of auditory cells is
due to the so called flexoelectricity, an effect similar to piezoelectricity, but manifested in the plasma
membrane of cells. When the cellular membrane of auditory cells is deformed by sound vibrations a
spatial separation of bound electric charges occurs generating electric voltage across the membrane.
The direction from which the sound comes also carries important information. Its determination in
humans is based on the following physical effects. Sound first arrives in the auricle where it sustains
diffraction and slightly changes its acoustic spectrum. Due to the shape of the auricle, the diffraction
pattern depends on whether the sound is coming from the zenith to ear or from the nadir to ear. This is
how the position of the sound source in the vertical (sagittal) plane is established.
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
Fig. 3.3.4. The length of the outer auditory cells as dependent on their position on the basilar
membrane.
A - cells of the bat cochlea at the place detecting 160 kHz,
B - cells of the cat cochlea at the place detecting 40 kHz,
C - cells of the human cochlea at the place detecting 20 kHz,
D - cells of the guinea pig cochlea at the place detecting 5 kHz,
E - cells of the guinea pig cochlea at the place detecting 2.5 kHz,
F - cells of the guinea pig cochlea at the place detecting150 Hz,
G - cells of the human cochlea at the place detecting 40 Hz,
H - cells of the rat cochlea at the place detecting 15 Hz.
The disposition of the sound source in the horizontal plane is determined using two auditory
organs, this is the so called binaural hearing. The binaural effect is the listener’s ability to determine the
direction from which the sound comes in the horizontal plane by the usage of two ears. Fig. 3.3.5 shows a
sound wave traveling from a sound source to the listener. Obviously, the sound travels different path
lengths, S, befor reaching the two ears, S = d.cos . In this formula, d is the basis (the distance between
the two ears). Deviding S by the sound velocity we obtain the time delay, t, between the arrivals of
sound in the two ears. When  = 0° the time delay is maximal and at  = 90° it is zero. In addition, sound
arrives in the remote ear with lower amplitude, as the head is casting an “acoustic shadow” on this ear.
This is the so called baffling effect, resulting in the decrease of sound intensity in the ear, placed farther
away from the sound source. Thus, sound arrives in the remote ear with a time delay, t, and with reduced
amplitude, which both are used by the brain to establish the location of sound source in the horizontal
plane. Spatial resolution is the minimum angle between two sources that are perceived as different. Brain
has the smallest perceived time delay of about 0.02 to 0.03 ms which corresponds to a spatial resolution of
about a 2° to 3° angle.
There are sometimes abnormalities in hearing ability of humans. They demonstrate themselves as
a reduction in the dynamic range of the hearing, increase in the minimum threshold of audibility and
decrease in the pain threshold. Such cases could be found in young children with congenital impairment,
after certain infections, industrial accidents and in the elderly. This defect can be alleviated applying
auditory (hearing) prosthesis. The latter consists of a microphone, an electronic amplifier and headset.
The microphone converts sound vibrations into electrical signals, whose power is amplified by the
amplifier which uses the energy of electric battery. Headset is placed in the ear and converts amplified
electric signals into sound. The main unit of the auditory prosthesis is the amplifier which makes possible
to percept weak sounds, to correct the perception of the sounds with certain frequencies and to compress
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
sounds with greater intensity. In order to convey the real timbre of the sounds the amplifier should avoid
any frequency and amplitude distortions, i.e., it must equally amplify signals which strongly vary in
frequency and amplitude. With old analog amplifiers, however, this is hardly feasible. The recent digital
amplifiers provide virtually no distortion of the amplified signal.
Fig. 3. 3. 5. The determination of the
direction of the sound in the horizontal plane
is based on the binaural effect.
Another modern way to correct hearing
is the hearing implant, which is applied in the
case of serious damage to the eardrum and
middle ear. It consists of external and internal
parts (Fig. 3. 3. 6). The external unit contains a microphone and a microprocessor which amplifies the
electrical signals of the microphone and encode them in a series of impulses. By means of an outer coil,
these impulses are transferred to the inner coil (the receiver) placed behind the cranial bone. Impulses
captured by the receiver compel the vibrator to oscilate. These vibrations are sent to a vibrating plate
which, depending on the location of hearing damage, is mounted either on the first ossicle (the hammer) or
directly on the oval window.
There is another variant of hearing implant frequently applied recently. It differs from the above
described in its internal unit. Impulses captured by the receiver coil are sent into a bundle of wire
conductors (between 4 and 22 in number) that
are implanted directly into the cochlea along
the basilar membrane. Thus, the signals reach
the different regions of the basilar membrane
and irritate the respective auditory cells.
Fig. 3. 3. 6. Scheme of hearing
implant.
3.4. Physical basis of speech production. Speech apparatus in humans. Sound units.
Pronunciation of vowels and consonants, voiced and voiceless phonemes. Frequency spectrum and
formants of the sound units
Speech is characteristic human physiological process performed by the speech apparatus. The
speech consists in the production of prolong and complex concequences of sounds, which convey
information to other people. The shortest, inseparable parts of speech are called sound units (phonemes).
In most modern writing systems each phoneme is marked with a sign (letter). In general, the phonemes are
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
vowels (A, E, I, U, O, ə and their variants) and consonants (B, C, D, G, H, K, L, M, N, P, Q, R, S, T, V,
X, Z, CH, SH and their variants).
Phonemes build up words and the words are organized in sentences according to certain linguistic
rules. There are thousands of languages on Earth, which use practically the same phonemes but different
words to describe the same things, and different linguistic rules for compiling sentences. The number of
phonemes in different languages varies between 25 and 45. For example, the English word PHYSICS
contains six separate phonemes: F, I, Z, K and S, one of which (I) is repeated. Phonemes in different
languages differ slightly from one another. For example, the phoneme A is present in all languages and
has practically the same sound content in them. Some languages do not contain a certain type of
phonemes, for example Chinese language does not contain the phoneme R, the phoneme P is absent in
Arabic, Türk languages do not use the phoneme TS and so on.
To produce phonems and
words the speech apparatus in human
uses some organs which are part of
other
physiological
systems
(respiratory, digestive). These organs
are the lung, trachea, epiglottis,
larynx, tongue, soft palate, lips, teeth,
nasal cavity (Fig. 3.4.1).
In general, the speech
apparatus can be divided into two
parts. The first part contains lung,
trachea and larynx, and the other part
consists of the oral and nasal cavities.
The first part produces periodic
vibrations in the outbreathed air while
the second part filteres and converts
these vibrations into final phonemes.
Lungs
and
associated
muscles act as a source of airflow for
exciting the vocal cords. Muscle force pushes air out of the lungs like a piston pusihing air out of a
cylinder. The air passes through the bronchi and trachea in which the larynx is located (Fig. 3.4.1). Larynx
contains two plate-shaped muscles, called vocal cords. The vocal cords are always connected at one of
their two ends, while the opposite ends are free and can be spread apart and bring together (Fig. 3.4.2). At
breathing and exhaling these two ends are maximally separated and trachea is wide open. This allows air
to easily move to and from the lungs. In speaking and singing these two ends are tightly clinged to each
other whereby the vocal cords close the trachea like valve.
Lung is the source of energy for pronouncing phonemes. The air flow coming out of the lung
during exhalation have a laminar form. After passing through the larynx, the air flux changed depending
on whether the vocal cords are open or closed.
When the vocal cords are open the laminar air flux in front of them changes into turbulent flow
after them. This turbulent flow also represents mechanical wave, although it has very small amplitude of
vibration and broad, continuous frequency spectrum. The separate vortices of the turbulent flow represent
weak mechanical oscillations with small amplitude. Their frequencies are uniformly and densely
distributed in a wide range. This type of mechanical wave is called white noise and is exemplified by the
wind. The air flow after the vocal cords is turbulent in two cases, when pronouncing the so called
voiceless (unvoiced) phonemes and at whispering.
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
Fig. 3.4.2. Elements of human vocal tract (A). Cross-section of the larynx at breathing and
exhalation showing widely opened vocal cords (B). In speaking and singing vocal cords are tightly
clinged to each other.
The air flow coming out of the closed vocal cords has strongly interruptive, alternating character,
i.e., it represents a periodic mechanical sound wave with high amplitude. How to explain this? When
vocal cords adhere to each other, the flow of exhaled air compels them to vibrate. In turn, this vibration
tears the air flow into separate portions (Fig. 3.4.3). When the air flow reachs the vocal cords, being in
completely closed position, the pressure starts to climb up until the cords become pushed apart. Then a
small portion of air passes through the channel formed between the cords (Fig. 3.4.3 - a, b). This portion
of the air, however, moves at high speed. Accoding to the effect of Bernoulli (the high velocity of fluid is
associated with low pressure), the pressure starts to decrease until it becomes lower than the muscle force,
which holds the cords together (Fig. 3.4.3 - c, a). Thus, the vocal cords are allowed to return to their
closed position, the air flow interrupts and the pressure again stars to increase. The cycle of opening and
closing the cords repeats many times over one second, producing multiple airflow interruptions, i.e, a
mechanical wave with large amplitude that moves up the trachea. The vibration of the vocal cords can be
felt tuching the Adam's apple with finger.
Phonemes, produced when the vocal cords vibrate are designated as voiced. Phonemes,
pronounced without vibration of the vocal cords, just by turbulent air flow, are referred to as voiceless
(unvoiced). A part of the consonants are always voiced, these are B, G, D, L, M, N, ZH, Z, R and others.
The remaining consonants are always unvoiced, these are P, K, T, CH, SH, etc. The vowel phonems can
be pronounced by the two mechanisms - by vibration of the vocal cords and by turbulent flow (in
whispering). Thus, vowels are voiced when spoken with strong exhalation and vibrating cords, and
unvoiced when spoken in quiet whisper. Whisper is a speech with weak force, when the vocal cords
produce a turbulent airflow without major vibrations. The voiced consonants can not be pronounced
properly in whispering, for example each voiced consonant is pronounced and heard as its corresponding
unvoiced one: B as P, G as K and D as T.
The degree to which the vocal cords should be extended and either voiced or unvoiced phoneme
should be pronounced is controlled by the rate of the nerve impulses sent by the speech center of brain.
The periodic mechanical wave generated by closed, vibrating vocal cords represents a complex
musical tone, which contains a sum of vibrations with frequencies associated with one of them. The
lowest frequency of vibration is called fundamental frequency - fo. The other frequencies are multiples of
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
the fundamental - 2fo, 3fo, 4fo, 5fo, etc. and are referred to as harmonics. There are no overtones, i.e.,
vibrations with frequencies different from the fundamental one and its harmonics. Actually fo is the
frequency at which the vocal cords vibrate. At speaking, the fundamental frequency, fo, varies slightly and
usually has a low value (about 120 Hz for men and 140-150 Hz for women). At singing, fo strongly
increases depending on the pitch of tones.
Fig. 3.4.3. The vocal cords form a relaxation oscillator. Air
pressure builds up (a) and blows them apart (b). Air starts to flow
through the orifice and, due to the Bernoulli effect, causes the pressure
to drop down allowing the vocal cords to close again (c). Then the cycle
is repeated.
To increase the fundamental frequency, fo, the vocal cords become
stronger stretched narrowing the channel between them and reducing the
area of the surface that vibrates (fig. 3.4.4). Depending on the distance
between the vocal cords and their stretching four conditions are
distinguishable that are termed mode M0 (widely distanced vocal cords, no
vibrations – breath mode), mode M1 (clinged vocal cords, slight stretching, vibrations with low frequency,
the vibrating area is large – speech mode), mode M2 (clinged vocal cords, the stretching is strong,
vibrations have high frequency and the vibrating area is reduced – singing mode) and mode M3, which
occurs only in rare ocassiones (clinged vocal cords, the extension is maximally possible, the vibrations
occur with very high frequency - screaming).
The mechanical wave or turbulent flow, produced after the vocal cords both come out to
atmosphere usually through the oral cavity (fig. 3.4.1). In rare cases, when the nasal phonemes are
pronounced, the velum (soft palate) closes and deviates the air flow from the mouth to the nasal cavity.
Accordingly, the second part of the speech apparatus contains the oral and nasal cavities. The role of the
oral, respectively, nasal cavity is to change the frequency spectrum of air flow vibrations, whereat the
oscillations having a certain frequency increase their amplitude (resonance) and oscillations with other
frequencies become subdued. This process is referred to as filtration (articulation) of the sound. The type
of filtration depends on the position of many organs involved; the tongue, lips, teeth, hard and soft palate,
all called articulators.
The position and arrangement of articulators is different and specific for each phoneme and it is
also controlled by the neuro-electrical impulses sent by the speech center of brain.
The physical meaning of filtration is to modify the spectrum of air flow vibrations creating several
distinct groups of oscillations each having close frequencies and amplified amplitudes. These groups of
enforced vibrations are called sound (acoustic) formants (Fig. 3.4.5). Each phoneme contains several
sound formants (up to seven), separated by frequency intervals where oscillations are strongly suppressed.
Due to their large amplitudes the first several formants are of prime importance in distinguishing the
different phonemes.
Fig. 3.4.5 shows an example of frequency spectrum of a periodic mechanical wave generated by
vibrations of the vocal cords in mode (M1). The sound harmonics are evenly spaced from each other and
have decreasing amplitudes. After passing through the mouth cavity each oscillation, depending on its
frequency, is filtered out in a way dependent on the position of articulators. The same type of filtering is
obtained when the larynx produces a turbulent flow, instead of periodic mechanical wave. In this case,
however, the amplitude of vibrations is much weaker. It is shown on the figure, that the filtration elicits
the appearance of two formants, the first one centered at 500 Hz, and the second one at about 1500 Hz.
Phoneme with such a spectrum, containing two formants at 500 Hz and 1500 Hz, corresponds to the vowel
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
sound A (Fig. 3.4.5). Other vowel sounds contain similar spectra with two main formants, but centered at
other frequencies depending on the position of articulators.
Fig. 3. 4. 4. Position of the vocal cords during free breathing (A), production of high tone (B)
and production of low tone (C). A - The vocal cords are separated. The air passes freely between the
cords, there is no vibration and sound. B - The vocal cords are clinged and highly stretched in
length. Airflow compels the vocal cords to vibrate at high frequency due to the strong extenssion. C
- The vocal cords are clinged and slightly elongated. Airflow compels the vocal cords to vibrate with
low frequency due to the low extenssion.
Fig. 3.4.6 shows the frequency intervals of the first two formants of all English vowel sounds.
This plot is constructed by two perpendicular axes, corresponding to the frequencies of the first and
second formants, respectively. The first formant of vowels varies in the frequency range from 300 to 1200
Hz, while the second formant is located higher, between 800 and 3000 Hz. As shown, each vowel is
represented by a specific area (ellipse, oval) in this plot. These areas do not overlap, allowing the human
ear and the auditory center in the brain to recognize and distinguish each vowel as a separate sound event.
Fig. 3.4.5. Frequency
spectrum of the mechanical
wave, generated by the vocal
cords, and its change after
passage of the wave through the
oral cavity.
When different people
pronounce the same vowel, the
frequencies of the two formants
do not completely coincide. For each individual these two frequencies represent an individual point within
the respective area (ellipse) as shown in Fig. 3.4.6. Because the area of each of these ellipses is quite large,
individuals may have large differences in the frequencies of formants corresponding to the same vowel.
This affects the timbre of individual voice and enables the determination of the personality of speaker.
Upon singing of a certain vowel the stretching of vocal cords increases depending on the pitch.
With increasing the stretch the fundamental frequency of the vibrations of the vocal cords increases. The
frequencies of both formants, characteristic of this vowel, also increase, however, their ratio remains the
same. In other words, upon singing a given vowel with higher or lower pitchs its frequency spectrum
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
moves up or down the frequency axis, but its appearance is retained. This result allows the conclussion
that the perception of a given vowel depends on the ratio of the frequencies of its formants and does not
depend on the absolute values of these frequencies.
Compared with vowel sounds the filtration (articulation) of consonants is much more complex and
diverse. Therefore, the frequency spectrum of consonants is more complex than that of vowels.
Consonants usually contain more than two significant formants. As above mentioned, the consonants are
voiced or voiceless depending on whether or not the vocal cords vibrate. On the other hand, depending on
the type and place of articulation, the consonants are divided into plosives, fricatives, nasals, palatals and
others. The nasal consonants (M, N and NG) are produced when the air flow passes through the nasal
cavity (fig. 4.3.1). The fricatives (F, K, D, G, S) are produced pushing a constant air flow through the
narrow channel made up by placing two articulators close together, for example between the tip of the
tongue and lower jaw. This channel generates a strong turbulent flow with wide frequency range. Special
part of the fricatives constitute the so called sibilants or
affricates (CH, ZH, SH, Z).
Fig. 3.4.6. Frequency intervals of the first two
formants of all vowels sounds in the English language.
Plosive consonants are produced in two stages.
During the first stage there is a full occlusion of air flow to
both the mouth and nasal cavities. During the second stage
the airflow is abruptly released, which generates short but
strong turbulent flow with a wide spectrum resembling that
of an explosive outbreak. The type of consonant produced
depends on the location of the blockage, for example the
contraction of the lips produces P and B. Various plosives are produced when the palate is tuched by a
special part of the tongue (the front part -T and D, the middle part – K, and the back part – G and H).
However, the vibration of vocal cords is obligatory in the production of voiced plosives - B, D and G.
When the speech apparatus is arranged to produce some of these voiced consonants and the vocal
cord do not vibrate the so called unvoiced consonants are produced; P instead of B, T instead of D and
K instead of G.
Besides their frequency spectrum, vowels and consonants differ in their duration over time.
Vowel sounds are pronounced with longer duration, while consonants are shorter. This feature
highlights the different roles of vowels and consonants in speech. Due to their rich spectrum the
consonants are better recognizable and bring more information compared to vowels. Therefore
languages that are richer in consonants, as the Slavic and Latin languages, are better intelligible
compared to those that are rich in vowel sounds, such as the languages of the German group. In turn,
vowel sounds are more important in singing, as they better emphasize the pitch of different tones.
In some languages (French, German) the different vowels can be open or closed depending on
their place in words. In some languages (Bulgarian) the length of each vowel sound is the same in all
words. In other languages (Finnish, German, Czech, Serbian) vowel sounds are long and short, which
changes the meaning of the word. In German, Czech and Serbian long vowels last two times the
shorter ones. In Finnish language, this ratio is 3:1. In some so called musical languages (Chinese and
related) the fundamental frequencies of the vowel sounds change, upwards or downwards, imparting
different sense to the words.
3.5. Ultrasound and infrasound - physical basis of their biological activity. Production and
therapeutic applications of ultrasound in medicine
Ultrasound is an elastic oscillation of material media at a frequency of 20 kHz to about
60 MHz. Sourses of ultrasound are waterfalls, wind, sea waves, mountain streams, some machines and
animals. Ultrasound with frequencies up to 100 kHz is obtained using the magnetostrictive effect (Fig.
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
3.5.1). The electric current flowing in a coil creates an alternating magnetic field. This in turn causes the
core, made up of a ferromagnetic material (iron, nickel), to change its shape and size with the same
frequency (magnetostriction effect), generating vibrations in the air.
Fig. 3.5.1.
Generation
of
ultrasound based
on
the
magnetostrictive
effect (A) and on
the piezoelectric
effect (B).
Modern
medicine
uses
preferably
the
piezoelectric
effect to generate and detect ultrasound, based on the deformations of the so called piezoelectric materials.
They include ionic crystals of the type quartz, barium titanate, tourmaline, Rochelle salt, ammonium
phosphate, some ceramics and biological tissues (bones, DNA). In the absence of external force and
deformation the ions of these crystals are arranged so that their opposite charges neutralise each other
(Fig. 3.5.2). Consequently, there are no free volume charges at rest. Applying an external deforming force,
however, the ions are displaced yielding spatial separation of electric charges. Therefore, uncompensated
volume charges of opposite sign arise (dielectric polarization) and electric voltage appears on the opposite
sides of deformed crystal (Fig. 3.5.2). This phenomenon constitutes the direct piezoelectric effect which is
used in ultrasound sensors (detectors or transducers). When ultrasound wave reaches this device its
piezocrystal sustains periodic deformation with the frequency of ultrasound wave and this oscillaton
generates alternating electrical signal which is measured.
Fig. 3.5.2. Stretching – compression deformation of quartz crystal. Some of the links are
more deformable (shown with a double line), which is the cause for uncompensated volume charges
to appear.
When an external electric voltage is applied on a piezocrystal, the piezocrystal deforms, this is the
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
converse piezoelectric effect. The latter effect is used in the ultrasound emitters. In this case, the
alternating electric current coming from an electric generator, produces a periodic deformation of the
piezocrystal which generates a mechanical wave at a frequency equal to the frequency of the current. In
order to have more efficient conversion of electrical energy into mechanical energy, the frequency of the
electric voltage must be equal to the natural frequency for oscillation of the quartz plate.
In medicine, ultrasound is used in diagnostics, therapy and surgery. The key physical parameters
of the ultrasound, which are crucial for its medical applications are:
1. Speed of propagation, C. The ultrasound speed is different for different media (Table. 3.5.1), in
the air it is considerably lower than in condensed media (tissue, water). The condensed matter allows the
propagation of transverse and longitudinal waves, whose velocities are different.
2. Acoustic resistance Z = .C. It depends on the density, , of the medium and on the speed of
propagation, C. The acoustic resistance depends on the composition and structure of the tissue and is
different in different tissues. Therefore, the boundary between two different tissues reflects the ultrasound;
the intensity of the reflected beam is greater when the difference between the acoustic impedances of the
tissues is greater. The acoustic impedance of tissues is about 3500 times greater than that of air. The
acoustic impedance of the bone is so great, that the ultrasound does not practically penetrate into them,
making impossible ultrasound diagnostics of bones. In ultrasound diagnostics and therapy ultrasound
source directly contacts the skin of the patient through a contact gel, to avoid the strong reflection of the
beam on the interface between air and the body. Water, glycerin, petrolatum, paraffin and their mixures
are used as a contact gels.
3. Intensity of the beam. This is the density of acoustic energy the ultrasound brings. In diagnostic
applications, it is from 10 to 50 W/ m2.
4. Generation mode. It is of two types, continuous (accompanied by thermal effect) and pulse (no
thermal effect is produced).
5. Depth of penetration. It shows the distance into tissues where ultrasound fades to 65%. The
depth of penetration strongly depends on the frequency of the ultrasound. At 0.8 MHz it is about 3-4 cm
and at 3 MHz it is only 1.5-2 cm.
The mechanism of biological action of ultrasound is mainly determined by three physical effects.
The most important applications of ultrasound are based on its mechanical effect - this is the mechanical
oscillation, the compression and rarefaction of the constituent particles of the medium (micro massage)
and the associated change in pressure. For example, at a frequency of 1 MHz the ultrasound pressure in
water changes by about  2 ata. This facilitates and enforces diffusion. At intensities of about 1000 times
greater than the diagnostic ones (more than 30 kW/m2) the ultrasound induces additional effects, heating
of the medium (thermal effect) and cavitation in the liquid media. The moderate thermal effect (1-3 оС) is
useful because it increases the activity of enzymes and accelerates the transport processes. In liquid media
ultrasound causes cavitation, which represents cycles of appearance and disappearance of bubbles filled
with water vapor. As the bubbles continuously form and disappear in tact with the mechanical wave, the
atoms and molecules of water vapor become
ionized generating free radicals that oxidize
Tab. 3.5.1. Speed of ultrasound in
different media at 20 °C
biological macromolecules present (chemical effects
of ultrasound). Upon the closure of bubbles very
Speed of ultrasound
high pressure results, that destroys the suspended
Medium
(m/s)
cells and biomacromolecules. This is used in the
ultrasound homogenizers and disintegrators. At very
Air
330
high frequencies ultrasound causes microvibrations
Water
1497
of intermolecular bonds in biomolecules.
Blood plasma
1520
The physico-chemical effect of ultrasound
Soft tissue
1540
consists in the increase in the permeability of cell
Bones
2700 - 4100
membranes. In higher organisms an nervous reflex
Blood
1570
Muscle
1500 - 1630
and neuro-humoral action of ultrasound occur.
Fat
1440
The reflection of ultrasound at various
Metal
3000-6000
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
discontinuities and its ability to pass through the soft tissues without substantial absorption is used to
diagnose the inner organs of human body. Under certain conditions and parameters, ultrasound has
therapeutical effect. Low power ultrasound causes micromassage of tissues, activation of metabolism and
moderate local heating, which has a therapeutical effect. Surgery uses high power ultrasound to destroy
tissues, tumors, kidney stones, etc., to conect bones and for painless drilling holes in bone, etc.
1. The application of low intensity ultrasound (1 W/m2) has a curative effect. It enhances the
passive transport, improves trophics, increases permeability of tissues and membranes, accelerates
immune response. These effects are associated with the mechanical and physicochemical effects that accompany the passage of ultrasound through tissues.
Fig. 3. 5. 4. Non-operational treatment of brain tumors using lowintensity ultrasound beams focused on the therapy volume.
2. The application of mechanical wave and ultrasound
accelerates the healing of broken bones, according to a discovery of Bulgarian
doctors. Ultrasound accelerates the regeneration of connective tissue, bone and
soft tissue.
3. Ultrasound improves the activity of muscular system and the peripheral nervous
system.
4. Ultrasound has an analgesic effect in the diseases of nervous and skeletal systems and
muscles, and of the gastrointestinal tract. It normalizes excitability, improves trophics and has
antispasmodic action.
5. Ultrasound facilitates the penetration of drugs through the intact skin and directs them
immediately into the therapeutical zone (phonophoresis). The drug is dissolved in lanolin, petrolatum and
etc. It is successfully applied in sciatica.
6. Ultrasound is used for non-invasive treatment of tumors located in the depth of human brain
(fig.3.5.4). Because ultrasound hardly penetrates bone tissues, including the skull bone, a large number of
rays are directed to the tumor. After passing through the bone, each beam has a low, subcritical intensity
and is safe for the brain tissues. All the rays are focused in the tumor, their energy is collected exceeding
the critical limit and the tumor is irreversibly impaired.
7. The thermal effect of high intensity ultrasound is used for cutting tissues. This action of
ultrasound is used in the bloodless ultrasound scalpel. The scalpel emits powerful ultrasound beam that
overheats the tissue under the scalpel and the proteins denature. Simultaneously with protein denaturation,
the damaged tissue is destroyed by the mechanical action of ultrasound. On the other hand, the denatured
proteins adhere (coagulate) clogging the small and medium-sized blood vessels strongly reducing
bleeding. This is called haemostatic effect of ultrasound scalpel.
8. The ultrasound sonicators (disintegrators) use high intensity ultrasound which lyse and kill
animal cells and bacteria. Such devices are used for sterilization of utensils and tools, degreasing and dry
dishwashing, fragmentation and emulsification of insoluble drugs and production of sols in
aerozolotherapy.
9. A constriction or plaque, formed in a blood vessel or in a bile duct can be removed by
an ultrasound emitter. A miniature ultrasound emitter is mounted on the tip of a catheter drived through
the vessels close to the constriction. Reaching the constriction, the catheter switchs on the ultrasound
generator and the emited ultrasound destroys the constriction.
Usually the range from 16 to 25 Hz is considered as the upper frequency limit of the infrasonic
waves, while the lower limit reached 0.001 Hz. Sources of infrasound are electrical discharges in the
atmosphere, waterfalls, sea waves, wind and turbulent motions of the atmosphere, explosions, cannon
shots, jets, volcanic eruptions and earthquakes. The sounds of various machines, engines and vehicles
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
contain infrasonic waves.
Infrasound has a very long wavelength. For example at a frequency of 3.5 Hz its wavelength is
about 100 m. Due to its low frequency and long wavelength the infrasound is absorbed very poorly and
bypasses the barriers of significant size. This allows its spread at distances up to several kilometers.
Several big animals (elephants, crocodiles, hippos) use the infrasound as a means of long range signaling.
As a rule, infrasound energy is absorbed very poorly by the tissues of human body. However, it is
not harmless to humans. The problem is that some important internal organs (brain, lungs, liver, heart)
have natural frequencies of oscillation in the range between a few Hz to 12 Hz and the passage of
infrasound through the human body may cause a resonance with these organs. In case such resonance
occurs, the energy of infrasound is continuously absorbed by the organ and its forced vibrations increase
over time. The most dangerous is infrasound with a frequency between 6 and 9 Hz, which is absorbed by
the heart, lungs and brain. The prolonged action of low intensity infrasound induces vomiting, tinnitus,
dizziness and feeling of causeless fear. Infrasound with middle intensity impairs breathing and digestion,
while high intensity infrasound can stop the heart. Infrasound at a frequency of 7 Hz coincides with the
alpha rhythm of the brain, and depending on its intensity causes fatigue, fear, psychotropic effects,
thinking disturbances and panic. Infrasound is deadly dangerous for jellyfish, relatedly they have
developed microscopic sensors detecting infrasound with frequency between 8-13 Hz. There are reports
that low intensity infrasound with the frequency of 15-20 Hz is safe and produces a beneficial effect on
the tissues and organs of human.
3.6. Ultrasound diagnostic methods - echography, sonography and doplerography
The most important application of ultrasound is the ultrasound diagnostics of various internal
organs. In this case, the ability of ultrasound to penetrate deep in the soft tissues of the body and to be
reflected by non-uniformities in them is used. Due to its very small wavelength, , (mm and parts of mm),
the ultrasound propagates in human tissues similar to the propagation of light rays in air. In addition,
ultrasound reflects and refracts on the interfaces like the light rays do. On the other hand, the high
frequency of ultrasound causes its significant absorption by the human tissues.
The ability of human tissues to reflect and absorb ultrasound depending on their structures is used
for obtaining a visible image of the internal organs (ultrasound diagnostics). The quality of obtained image
depends on the spacial resolution which is the shortest distance between two points of the observed object
still observable as separate. This distance approximately equals , therefore, in order to obtain a better
resolution ultrasound with high frequency (several MHz) and low  is used for diagnosis.
Ultrasound echography uses such an ultrasound beams which are readily reflected by internal
structures having the size of human internal organs. On the other hand, such a beam is absorbed strongly
by the tissues, which represents the physical basis of ultrasound sonography. Ultrasound with such a
frequency, however, has a small depth of penetration (a few cm), which requires a large amplification of
the reflected signal.
Fig. 3. 6. 1. Absorption of mechanical wave by a wall with
thickness X.
Modern medicine uses three basic methods for ultrasound
diagnosis.
1. Ultrasound echography. When a sound wave with an initial intensity, Io, passes through a
layer with a thickness, x, the energy of the wave is partially absorbed (Fig. 3.6.1). As a result, the
intensity, I, of the transmitted wave decreases: I = Io.exp (-a.x. 2). The linear coefficient of attenuation of
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
the sound wave, , depends on the interactions between the constituent particles of the absorbing layer.
This formule indicates that mechanical waves (ultrasound), having higher frequencies, will be absorbed
and diminish more strongly than those with lower frequencies (sound and infrasound). Compared to
ultrasound, infrasound and sound are practically not absorbed by the human body and, therefore, they
could not be used for diagnostic purpose.
Fig. 3. 6. 2. Reflection and refraction of ultrasound
beam at the interface of two media.
Interestingly, the layers consisting of gas have much
greater absorption ability () than the layers of condensed
matter (liquids, solids). This is due to the much weaker
interactions between the molecules of the gas, preventing the
transmission of vibrations from one molecule to the next one.
For example, the air absorbs ultrasound about 1000 times greater, than the layers of fluids and tissues of
the same depth. In medicine, the absorption of ultrasound by the air layer, located between the ultrasound
source and the patient, and the reflection of this ultrasound on the patient's skin are avoided, putting the
source of ultrasound in close contact to the body.
In media with different elasticities and densities, , the ultrasound propagates with different
speeds, C. The product C = Z is designated as acoustic impedance of the medium. When the ultrasound
beam reaches the interface separating two media with different acoustic impedances it become partly
reflected and refracted. Fig. 3.6.2 shows the refraction and reflection of the ultrasound beam at the
boundary of two media. The medium 1 has a density, 1, and sound speed, C1. For the medium 2 these two
parameters are 2 and C2, respectively. The angle at which the beam is refracted depends only on the
difference in the velocities, C1 and C2. On the other hand, the intensity of the reflected beam depends
primarily on the density difference between 1 and 2. In conclusion, the extent to which a ultrasound ray
should be reflected and refracted at the boundary between two media depends on the difference in the
acoustic impedances of these media.
Fig. 3. 6. 3.
Outlook of various
apparatus for
ultrasound diagnostics.
The
ultrasound
beam
transmitted
through the human body
reflects at the boundary
of tissues with different structures. This is used for the ultrasound location of internal organs using
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
ultrasound echographs shown in fig. 3.6.3. The same principle is used in modern ultrasound
ehoencephalographs which can detect brain tumors, and in ultrasound scanners that controls the growth of
the fetus in uterus.
Fig. 3. 6. 4. Usage of a single
quartz plate as an emitter of
ultrasound pulses and as a receiver
of the reflected pulses.
Most
often
a
same
piezoelement, called an ultrasound
probe (transducer), is used for
generation and detection of ultrasound wave (Fig. 3.6.4). The ultrasound probe emits a series of packed,
continuous ultrasound signals (pulses). The duration of each pulse (τ, the duty cicle, approximately 1 s)
is much shorter than the time interval between the beginnings of two adjacent pulses (the pulse repetition
period, T, about 1 ms). Thus, if ultrasound pulse encounters a barrier and reflects backwards, the reflected
signal (the echo) will return to the probe at a moment when the probe will be at rest. The receved signal
will deform the piezocrystal which, based on the converse piezoelectric effect, will generate alternating
voltage. In such a case, the same quartz plate can be used to operate firstly as emitter of ultrasound pulses,
and later as a sensor receiving the reflected ultrasound echo (Fig. 3. 6. 4).
Fig. 3.6.5 depicts the structure of an ultrasound probe (transducer) used for the generation and
detection of ultrasound beams and echos. The alternating voltage is transmitted through a power cable to
the piezocrystal plate and compels it to vibrate. The ultrasound pulses are emitted and focused only
rightwards. In the opposite direction they are quenched by the sound insulator.
Fig. 3. 6. 5. Principle scheme of ultrasound probe (transducer).
Fig. 3.6.6 (A) illustrates the principle of obtaining ultrasound echographic image. Using an
ultrasound probe a beam of ultrasound pulses is directed towards the internal organ. The beam sustains
partial reflection from the walls of the internal organ. Thus, several echoes are produced having different
intensities and different times for arrival at the probe depending on the distance, L, between the reflecting
surfaces and the probe. The incident beam and the reflected rays can be seen on the screen of oscilloscope
as peaks located on the time axis at locations corresponding to their time delays (Fig.3.6.6 B). Provided
the time delay (t) of each refleted beam is precisely measured the depth, L, can be calculated using the
formule: L = 0.5. t. C, where C is the velocity of ultrasound in the tissue.
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
Fig. 3.5.6. Reflextion of the
ultrasound signal from various surfaces
of an internal organ (A) and
observation of the reflected signals on
the oscilloscope screen (B).
Fig. 3.6.7 shows the basic ideas
for image presentation in the different
types of ultrasound echography. In A –
mode echography (A comes from
amplitude) the intensity of the reflected
rays is given as the height of a peak on
time axis. Most often, however, the
intensity of the reflected signal is given as
a brightness of a shinning spot on the same
axis (B-mode echography). The distance (time intervals) between the peaks or bright spots determines the
depth of scattering surfaces (kidney, liver, lung, tumor mass). There is another presentation, M-mode
echography in which each bright spot on the time axis is sweeped in a vertical line. If the echo is reflected
from a stationary surface the sweeped spot yields a vertical straight line, however, if the echo comes from
a moving object (heart valve) a wavy vertical line is obtained.
2. Doplerography. This method is based on the Doppler's effect. In 1842, Austrian physicist and
astronomer Christian Doppler described the change in the frequency of mechanical and light waves when
they are reflected by moving objects. If the source of ultrasound and the detector do not move relative to
one another, the sound is received with the same frequency, o, as that of the emitted one. If the source
and detector move relative to one another at a speed, V, the sound is received with a different frequency,
, whereat,  = o/(1 ± V/C). Here, C is the sound velocity while the signs “+” and “-“ are used depending
on whether the emitter and receiver are distancing or approaching, respectively. The frequency change, 
= o - , is called Doppler frequency.
Similarly, if the ultrasound is reflected from an object, which is moving with the velocity, V,
relative to the stationary emitter and receiver, the frequencies of the incident beam and the reflected beam
will differ depending on the speed V. The Dopler frequency, , is given by the approximate formula 
 2. o .V/C, where C is the speed of sound.
In ultrasound doplerography the Doppler frequency is determined after the ultrasound is reflected
by a moving tissue (erythrocytes in the blood, heart valves, pulsating fetal heart, etc.). Erythrocytes of the
moving blood most offen play the role of the moving object in ultrasound Dopplerography. For this
purpose two piezoelements are used, whereat one generates the ultrasound impulses and the other receives
the reflected impulses (fig. 3.6.8). The Doppler frequency obtained is usually in the audible frequency
interval from 100 Hz to several kHz. Hence, the electric signal corresponding to the Dopler frequency is
amplified and put into a loudspeaker in order to be heard by the doctor. The pitch of the heard sound is
proportional to the speed of the blood cells or the heart valves. Thus, the doctor can determine the velocity
of blood in a vessel, and the presence of stenosis.
3. Sonography. Passing through various media the ultrasound is absorbed depending on their
linear coefficient of attenuation, ., i.e., on their structure, composition and density. The ultrasound
sonography measures the intensity, I, of a sheaf of ultrasound beams passing through a human tissue.
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
Individual rays are absorbed to varying degrees, depending on the structure and properties of the tissues
they pass through. Large number of detectors, located behind the body of the patient, is used to measure
the attenuation of each particular ray of the sheaf. The data, provided by these detectors, are processed to
construct the image of the internal organs on a screen.
Fig. 3.6.7. Principle of producing ultrasound
echography image of types A, B and M. One of the objects
is moving, its movement is visible on the vertical wavy
line in the ultrasound echography M image.
Advantages and disadvantages of ultrasound
diagnostics. Compared to X-ray diagnostics, the ultrasound
diagnostics is faster and completely safe because it uses low
intensity and safe ultrasound beams. No harmful side effects are currently established. This type of
diagnosis does not use contrast agents, such as those applied in the X-ray, MRI and computerized
tomography, which are harmful to humans.
Ultrasound diagnostics, however, has two major drawbacks. Due to the very large acoustic
impedance and low elasticity of bone tissue, ultrasound is reflected and strongly absorbed by bones.
Therefore, ultrasound has a very low ability to penetrate into bones compared to soft tissues (muscles,
tendons, connective and fatty tissues) which are highly elastic and less absorb ultrasound. The above
explains why ultrasound is primarily used for diagnostics of internal organs composed of soft tissues. For
the same reason, tissues containing air bubbles (lung, rarely stomach) also reflect and strongly absorb
ultrasound beam. As a result, bones and lungs (and sometimes stomach) can not be diagnosed by
ultrasound.
Fig. 3. 6. 8. Schematic diagram
illustrating the ultrasound
Doplerography.
The second disadvantage stems
from the different velocities of
propagation of mechanical waves of
transverse and longitudinal types. When a sound wave moves in a solid body and meets inhomogenity on
his way, it sustains reflection and refraction at the boundary between two media. The reflected and
refracted waves both decompose into two components, one with transverse and the other with longitudinal
vibration of the particles. Because the longitudinal component moves at greater speed compared to the
transversal one, both components are refracted at different angles and reach the receiver (probe) at
different delay times. This produces two superimposed images. This is the main reason that deteriorates
the image quality in all types of ultrasound diagnostics.