Download CHAPTER 19 ACOUSTICS AND THE EAR

CHAPTER 19
ACOUSTICS AND THE EAR
19.1. MECHANICAL STIMULATION AND HEARING
Hearing is the detection and analysis of vibrations generated by objects at some distance
from the body transmitted to the ear as pressure waves in air, water, or other medium. Pressure
waves in air or any other medium are a form of mechanical energy. Sound cannot travel through
a vacuum because it depends on a medium such as air or water for propagation.
We depend on hearing to perceive information about vibrations that originate in sources
located far away from our bodies, to localize and identify sources of sound, and for
communication.
19.1.1 Physical properties of sound
19.1.1.1. Properties of vibrations in air. Many objects move in such a way that a regular
series of displacements, or vibrations, occurs. A vibrating object such as a guitar string, a
loudspeaker diaphragm, or your vocal cords, moves back and forth, displacing the air (or other
medium) around it. Vibrations from a sound source result in alternating condensation and
rarefaction of the air molecules. Condensation is an increase in the density of air molecules and
rarefaction is a decrease in the density of air molecules.
Figure 19-1. The diagram on the left shows the displacement of a loudspeaker diaphragm around its resting point as
a function of time. A gradual outward movement is followed by a gradual inward movement. The outward
movement pushes air particles closer together, increasing air pressure (condensation) and the inward movement
causes the air particles to spread farther apart, decreasing air pressure (rarefaction). This cycle repeats for as long as
the loudspeaker is producing a tone. The drawing on the right shows the effect of a vibrating loudspeaker
diaphragm on the surrounding air. Dark = high pressure; light = low pressure.
124
The pattern of condensation and rarefaction is propagated away from a vibrating source
much as ripples spread in water. The air molecules themselves do not move outward. What
moves are the peaks and troughs in air pressure. The resulting pattern of pressure changes can be
represented mathematically as a sine wave.
Figure 19-2. Properties of a mathematical sine wave function (left) and of sound waves transmitted through air
(right). The frequency of a pure tone sound (or other sine wave function) is the number of cycles completed per
second. The period is the time needed to complete one cycle. The wavelength is the distance between peaks (or
troughs, or any comparable part of a cycle), and depends on the speed at which the wave travels. The amplitude is
the difference in pressure between the peak and the trough of the waveform.
19.1.1.2. Properties of a sine wave. A sine wave can be characterized in mathematical
terms, based on the following measures:
EFrequency is the number of cycles completed per second, measured in Hertz (Hz). The
period is the time needed to complete one cycle, and depends on the frequency (1/frequency =
period). We perceive the frequency of a pure tone as its pitch. Humans can hear sounds from
about 20 Hz to about 20,000 Hz. Different animals have different hearing ranges.
Figure 19-3. Hearing ranges of different species. In general, larger animals (elephant) hear better at low frequencies
and small animals (mouse, bat) hear better at high frequencies.
E Starting Phase is the point in the cycle at which the wave starts, measured as phase
angle, expressed in degrees. A full cycle is 360 degrees. We do not perceive phase per se, but
when multiple sine waves occur simultaneously, the relative phases of the waves can result in
perceived changes in loudness, pitch, or quality of the sound.
125
E Amplitude is the amount of pressure change from the peak to the trough of the wave.
Amplitude is measured in decibels (dB). We perceive the amplitude of a sound as its loudness.
19.1.1.3. Interactions among sine waves. Most of the sounds that we listen to are not
pure sine waves. Instead, they are complex patterns of vibrations that can be mathematically
broken down into sine waves using a mathematical procedure called Fourier analysis. For this
reason, it is important to understand what happens when multiple sine waves occur together.
When the peaks, troughs, and other phase angles of sound waves occur simultaneously,
the waves are said to be in phase. When the peaks, troughs, or other parts of the waveform occur
at different times, the waves are said to be out of phase. Sound waves add together algebraically
so that two positive pressures (amplitudes) result in a higher peak, two negative amplitudes
result in a deeper trough, but a positive and a negative amplitude cancel each other. As a result,
waves that are in phase reinforce each other and waves that are out of phase cancel each other.
Figure 19-4. Two sine waves of the same frequency, starting out of phase, will always maintain the same phase
relationship, so that the interaction of the two waveforms, resulting in a periodic change in the amplitude of the
sound, will repeat itself with the same period and frequency as the waveforms themselves. Points C and D indicate
the times at which sine wave B and sine wave A cross the zero point during the downward half of the cycle.
Figure 19-5. If the frequencies of the sine waves were different, the higher frequency wave (solid line) goes
through more cycles in a given time than the lower frequency one (dotted line) so that the phase relationship is
constantly changing. As a result, periods when the two waves are in phase alternate with periods when they are out
of phase. The result is a periodic change in the amplitude of the sound, at a frequency different from either of the
two component waveforms.
19.1.1.4. The decibel scale. If we were to assign a value of 1 to the faintest sound that we
are able to hear, then the loudest sound that we can hear before experiencing pain would be
1,000,000,000,000,000 times as loud(which can also be written 1015. Because the dynamic range
of the ear is so great, sound amplitude is expressed on a ratio scale ( log10), not an interval
(linear) scale. The units of this ratio scale are called decibels (abbreviated dB), and are usually
126
referenced to the faintest 1000 Hz tone that can be heard (on average) by a young, healthy
listener.
Sound amplitude in dB = 20 log P1/P2
(where P1 is the pressure of the sound of interest and P2 is the reference pressure).
19.1.1.5 Sound fields. Sound moves out from the source in three dimensions, in a
spherical path. In air, sound travels at a rate of about 340 m/s. Sound travels slightly faster in a
hot humid place at sea level than in a cold, dry place at a high altitude. Sound intensity decreases
in proportion to the distance from the source.
19.1.1.6. How sound is modified by objects in the environment. Like light, sound
travels in a straight path from its source unless perturbed by objects in its path. Like light, sound
can be reflected from an object, transmitted through an object, deflected around an object, or
absorbed by an object. These modifications of sound by objects in its path play an important role
in sound source localization and our perception of the environment in which a sound occurs.
Figure 19-6. Interactions between sound and objects in its path. Left top: some objects transmit all or some of the
sound; left bottom: some objects absorb all or some of the sound. Right top: A very large object that does not
transmit or absorb sound reflects all of it; right middle: An object whose diameter is larger than the wavelength of
the sound reflects some sound but allows some to pass to the other side, creating a sound shadow. The larger the
object, the more sound will be reflected. Right bottom: An object whose diameter is smaller than the wavelength of
the sound allows all of the sound to pass over it.
19.1.1.7. Complex sounds. Naturally occurring sounds are almost never as simple as a
single sine wave. Complex waveforms can be broken down into multiple sine waves (each with a
different frequency, phase, and amplitude) using Fourier analysis. The frequency composition of
a sound is called its spectrum.. Frequencies in a complex sound that are an integer multiple of
some “fundamental” frquency are called harmonics.
127
19.1.1.8. Noise. Noise is a sound whose amplitude varies randomly over time; “white
noise” contains all frequencies over the audible range (or whatever range is relevant).
Narrowband noise contains only a selected band of frequencies.
19.1.1.9. Modulated stimuli. A modulation is a change in some parameter of a sound.
Amplitude modulation (AM) is a variation of the amplitude (loudness) of a sound. Frequency
modulation (FM) is a variation in the frequency (pitch) of a sound. Many common sounds
including music and speech contain multiple harmonics that change in both frequency and
amplitude over time.
When sounds originate from multiple sources, the waveforms from the different sources
combine so that a single complex waveform reaches the ear. This presents a formidable
challenge to the analytical capabilities of the auditory system, as will be shown in the sections on
sound localization and auditory scene analysis.
Figure 19-7. Addition of sine waves of different frequencies and amplitudes to form a complex wave. Sine waves
on the left are added together successively to produce the complex waveforms shown on the right.
Figure 19-8. In an amplitude modulated stimulus (left) the frequency remains constant but the amplitude varies. In
the example shown, the amplitude of a tone of a specific frequency (the carrier frequency) is varied up and down in
a regular way. In a frequency modulated stimulus (right), the amplitude remains constant but the frequency varies.
In the example shown, the frequency starts low and ends high.
19.2. THE EAR
128
The auditory system includes the outer ear (pinna), the middle ear, the inner ear, and the
central auditory nervous system. The outer and middle ear structures as well as many of the
structures of the inner ear are involved in collecting sound energy and distributing it to a receptor
array in the cochlea where transduction takes place.
19.2.1. The outer ear, or pinna
The fleshy external part of the ear, the part you see, acts like an elaborate funnel to
collect sound waves and direct them to the eardrum for transmission to the internal parts of the
ear. Because of its shape and composition, the external ear is a highly directional collector and
amplifier of sound. The amount of amplification varies as a function of frequency, and is most
pronounced over the range of frequencies contained in human speech. Because of the way the
ear is structured, the spectral pattern of amplification varies most depending on the elevation
(height) of the sound source, and whether the sound source is in front of or behind the head,
making the external ear an important source of information used to localize sound sources.
19.2.2. The middle ear
19.2.2.1. Structure of the middle ear. The middle ear consists of a number of different
structures. The eardrum, or tympanic membrane, is a thin membrane stretched across the ear
canal. It is is set in motion by sound waves.
Figure 19-9. A view of the peripheral auditory system showing the major features of the outer, middle and inner
ear, and the functions performed by each.
Vibrations are transmitted from the eardrum to the ossicles, a chain of small bones in the
middle ear. There are three ossicles, the malleus, incus and stapes. The stapes is the smallest
bone in the body.
The malleus (hammer) contacts the tympanic membrane.
129
The stapes (stirrup) contacts the oval window, the membrane-covered opening to the
inner ear.
The incus (anvil) is located between the malleus and stapes.
The middle ear cavity is filled with air. The Eustachian tube links the middle ear with the
nasopharyngeal cavity so that the middle ear can adjust to changes in atmospheric pressure.
Figure 19-9. Diagram of the middle ear showing the ossicles and other main features. The shaded area indicates the
middle ear cavity.
19.2.2.2. Function of the middle ear. The middle ear performs several important
functions. The first of these is adjustment to changes in atmospheric pressure, through the action
of the Eustachian tube. The second is impedance matching, or compensation for the difference in
impedance (the resistance to being set in motion) between the air in the ear canal and the fluidfilled space of the cochlea. Third, the middle ear helps protect the inner ear from damage by
excessively loud sounds.
Several factors contribute to impedance matching in the middle ear. First, the area of the
tympanic membrane is much larger than that of the membrane-covered opening to the inner ear
(the oval window). This difference in size means that pressure that was originally distributed
over a large area at the tympanic membrane is concentrated over a small area at the entrance to
the inner ear. Second, the ossicles act as a lever that increases the force exerted by the stapes on
the opening to the inner ear.
Although the main function of the middle ear is to provide amplification of the pressure
transmitted to the inner ear, the amount of amplification can be adjusted in order to protect
against damage due to ongoing loud sounds. Several small muscles in the middle ear help keep
the ossicles suspended. If a very loud sound occurs, a signal from the brain causes the middle ear
muscles to contract, making the ossicular chain stiffer and more resistant to movement. This
increase in resistance means that the vibrations that reach the cochlea are lower in amplitude
than they would otherwise be.
19.2.3. The inner ear.
The inner ear serves a dual function in that it is the sensory organ for both hearing and
balance. During development of the ear, part of the inner ear (the cochlea) becomes specialized
to detect vibrations in air and another part (the vestibular system) becomes specialized to detect
head position and movement. In this section we will consider only the cochlea, or auditory part
of the inner ear.
130
19.2.3.1.General structure of the cochlea. The part of the inner ear that contains the
receptor cells for hearing is the cochlea. The cochlea is the site at which vibrations of the stapes
and inner ear fluids are transduced to receptor potentials, which give rise to neural responses in
fibers of the auditory nerve.
The cochlea is a coiled bony tube that resembles a snail shell. It is located deep within the
temporal bone of the skull. In humans, the cochlea coils about 2.5 times.
Figure 19-10. The cochlea is like a coiled tube, the inside of which is divided into three compartments.
The cochlear compartments and fluids. If we were to cut a cross-section through the
uncoiled tubular structure of the cochlea, we would see that the inside of the tube is divided into
several fluid-filled compartments. These include the scala vestibuli, scala media, and scala
tympani.
The three cochlear compartments are separated from one another by two membranes. The
basilar membrane is the thicker of the two, and is where the auditory receptor cells are located.
It forms the floor of the scala media, separating it from the scala tympani. Reissner's membrane
is a very thin membrane that forms the roof of the scala media, separating it from the scala
vestibuli. At the apex of the cochlea, the scala vestibuli connects with the scala tympani. Thus,
the scala media forms a closed, fluid-filled sac coiled within the walls of the cochlea.
The composition of fluids in the three cochlear compartments is very different. The scala
vestibuli and scala tympani are filled with perilymph, with an electrical potential ~ 0 mV relative
to extracellular fluids. The scala media is filled with endolymph, a fluid that is rich in K+ ions
(electrical potential ~+80 mV relative to extracellular fluids).
Because the resting potential of the hair cell is about -70 mV, the potential across the top
of the hair cell is close to 150 mV. This is the highest potential difference found anywhere in the
body. This high potential difference provides for a wide dynamic range in electrical response.
131
Figure 19-11. Diagram of a cross section through one turn of the cochlea showing the cochlear compartments and
the potential differences between the fluids in each compartment relative to extracellular space outside the cochlea.
The stria vascularis is the organ that produces the endolymph.
The organ of Corti. The organ of Corti is located on the basilar membrane. It contains
the hair cells (auditory receptor cells). The upper surface of each hair cell is covered with small
hair-like structures called stereocilia. The base of each hair cell is contacted by processes of one
or more auditory nerve fibers.
There are two types of hair cells: inner hair cells and outer hair cells. The inner hair cells
are the main cells responsible for sensory transduction. They have good frequency resolution and
relatively high response thresholds (low sensitivity). The outer hair cells are probably involved
in adjusting the functional characteristics of the cochlea and regulating sensitivity to sound. They
have relatively poor frequency resolution and relatively low response thresholds (high
sensitivity). They may help sharpen the frequency tuning of inner hair cells by contracting and
adjusting the mechanical characteristics of the basilar membrane.
The stereocilia on each hair cell extend up into a fibrous structure called the tectorial
membrane. Beneath each hair cell are processes of spiral ganglion cells, the first neurons in the
system. The ganglion cell bodies are located in the spiral ganglion, a region in the center of the
cochlea, about which the coils turn. Each ganglion cell gives rise to a centrally-projecting
auditory nerve fiber.
Figure 19-12. The organ of Corti as viewed in a cross section through one turn of the cochlea.
132
Figure 19-13. Cochlear hair cells have bundles of stereocilia (stiff hairs) on their top side (the side nearest the
tectorial membrane). Their bottom side is contacted by processes of spiral ganglion cells. On the left is a drawing of
a whole hair cell with ganglion cell processes beneath it. On the right is an enlargement showing the stereocilia as
seen in cross-section through the area indicated.
133