Download A PROPAGATION OF SOUND IN SOLIDS.

A
TERM PAPER
ON THE
PROPAGATION OF SOUND IN SOLIDS.
AND IT’S MODE OF PROPAGATION.
BY
· ARC/07/0929. AJAKAYE,OLUWADAMILARE
JOHN.
·
ARC/07/0933. AKINNIYE, OLUBUKOLA
DOOSHIMA.
SUBMITTED TO,
THE DEPARTMENT OF ARCHITECTURE
SCHOOL OF ENVIRONMENTAL TECHNOLOGY,
THE FEDERAL UNIVERSITY OF TECHNOLOGY, AKURE, ONDO STATE.
IN PARTIAL FULFILMENT FOR THE REQUIREMENT OF THE AWARD OF BACHELOR
OF TECHNOLOGY IN ARCHITECTURE.
LECTURERS IN CHARGE,
PROF. OLU OLA OGUNSOTE.
ARC. GANIYU.
MAY, 2012.
PROPAGATION OF SOUND IN SOLID
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CHAPTER ONE
SOUND AND SOUND WAVES
1.0
INTRODUCTION.
1.1
SOUND.
Sound is a vibration travelling through air, water, gases and solid barriers
and sensed by the ear. It is also a thing that can be heard in the ear. Sound is also a
sequence of waves of pressures that propagates through compressible media like
air, water, and gases. Sound can also be propagated through solids but it needs
additional modes of propagation like reflection, refraction, diffraction and
diffraction.
1.2.1 SOUND WAVES.
Sound waves travel or propagate through vibrations. If one particle starts
vibrating, it will pass the movement on to other particles that are close to it. This
means that sound travels quickly through solids because the particles are closely
packed and can readily pick up movement from their neighbor. Sound waves travel
less quickly through liquids because the particles are close enough to pick up
vibrations but not as tightly packed as in solids. It travels slowest through gases
because their particles are much further apart; and it travels better in liquids
because the molecules in a liquid are much more densely packed than in air. Here,
the molecules can bounce off each other hence, amplifying the sound- which is a
wave.
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Fig. 1: Compression and rarefaction sound wave
One way that the propagation of sound can be represented is by the motion
of wave fronts-- lines of constant pressure that move with time, using the wave
diagram shown below. Another way is to hypothetically mark a point on a wave
front and follow the trajectory of that point over time. This latter approach is called
ray-tracing and shows most clearly how sound is refracted.
Fig. 2: Sound waves showing the wavelength.
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CHAPTER TWO
2.0 PROPAGATION OF SOUND IN SOLID.
2.1
PROPAGATION OF SOUND.
Propagation means the movement through something, in this case, “the
movement through a solid barrier”.
Propagation of sound is the transmission of acoustic energy through a
medium via sound waves. The propagation of sound can come as a result of sound
hitting a solid and some of the sound being reflected back from the surface of the
solid (surfaces like walls, floors, ceiling, furniture, e. t. c). Depending on the type
of barrier, it can also be refracted, diffracted or diffused bringing about a change in
the behavior of propagation.
Fig 3: Propagation of sound. (Reflection, refraction and diffraction.)
The behavior of sound propagation is generally affected by three (3) things:
v A relationship between density and pressure. This relationship, affected
by temperature, determines the speed of sound within the medium.
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v The motion of the medium itself. For example, sound moving through
wind. Independent of the motion of sound through the medium, if the
medium is moving, the sound is further transported.
v The viscosity of the medium also affects the motion of sound waves. It
determines the rate at which sound is attenuated. For many media, such as
air or water, attenuation due to viscosity is negligible.
2.2
SOUND PROPAGATION AFTER HITTING A WALL (SOLID).
When sound hits something soft or movable the energy of the wave front is
dissipated in moving the object around. If the object is rigid, like a wall, two things
happen. Part of the energy of the wave front will set up a wave front within the
wall; just how big a part is transmitted this way depends on the material the wall is
made of. The rest of the energy is reflected off the surface according to the same
rules that apply to light on a mirror. (The most important of these is that "the angle
of reflection equals the angle of incidence".)
Here's what happens in two kinds of situations, one in which the source of
disturbance is relatively close to the wall, and one in which the source is far
enough away that you don't notice the wave front is curved. Several repeated wave
fronts are shown in each example.
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Fig 4: Propagation of sound after it hits a solid wall.
2.3
PROPAGATION OF SOUND IN SOLID.
Solids are made up of particles (atoms) that do not move about because they
are very closely and tightly packed (touching each other) and held together by
strong intermolecular forces. Therefore, they are always in a fixed position and can
only vibrate in that fixed position; sending sound waves along its path very fast.
This means that sound waves is immediately transmitted by the vibrating particles
in a fixed position by hitting neighboring or close atom sending on the sound
waves from one atom to the other throughout the solid object.
2.4
MODES FOR THE PROPAGATION OF SOUND IN SOLID.
In air, sound travels by the compression and rarefaction of air molecules in
the direction of travel.
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However, in solids, molecules can support vibrations in other directions, hence; a
number of different types of sound waves are possible. Waves can be
characterized in space by oscillatory patterns that are capable of maintaining their
shape and propagating in a stable manner. The propagation of waves is often
described in terms of what are called “wave modes.”
In solids, sound waves can be propagated in four (4) modes based on the
oscillation of the particles, that is, the behavior of the particles. Sound can
propagate in solids as longitudinal waves, shear waves, surface waves, and in
thin materials, they can propagate as plate waves.
2.4.1 LONGITUDINAL WAVES.
In longitudinal waves, the oscillations occur in the direction of the wave
propagation, that is, the longitudinal direction. Because compression and dilation
forces are active in these longitudinal waves, they are also called pressure and
compression waves. They are also called density waves because the density of their
particles fluctuates as they move. Compression waves can be generated in liquids,
as well as solids because the energy travels through the atomic structure by a series
of compression and rarefaction (expansion) movements.
2.4.2 SHEAR WAVES.
In shear waves, also called transverse waves, the particles oscillate at right
angle or transverse to the direction of propagation. An acoustically solid material is
required in shear waves for an effective propagation and therefore, they are not
effectively propagated in materials like liquid or gases. Shear waves are relatively
weak when compared to longitudinal waves. In fact, shear waves are usually
generated in materials (solids) using some of the energy from longitudinal waves.
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The two modes of propagation most widely and commonly used in ultrasonic
testing (sound waves that are too high for humans to hear) are longitudinal and
shear waves. The particle movement that is responsible for the propagation of
longitudinal waves and shear waves is shown below;
Fig. 5: Particle movement responsible for the propagation of longitudinal and
shear waves.
These two types of waves have different speeds, and (for example in an
earthquake) may thus be initiated at the same time but arrive at distant points at
appreciably different times. The speed of compression-type waves in all media is
set by the medium's compressibility and density, and the speed of shear waves in
solids is set by the material's rigidity, compressibility and density.
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2.4.3
SURFACE WAVES.
In surface waves (or Rayleigh), the waves travel the surface of a relatively thick
solid material penetrating to a depth of one wavelength. Surface waves combine
both longitudinal and transverse motion to create an elliptic orbit motion as shown
in the image below. The major axis of the ellipse is perpendicular to the surface of
the solid. As the depth of an individual atom from the surface of the solid
increases, the width of its elliptical motion also decreases. Surface waves are
generated when a longitudinal wave intersects a surface near the second critical
angle and they travel at a velocity between 0.87 and 0.95 of a shear wave.
Rayleigh waves are useful because they are very sensitive to surface defects
(and other surface features) and they follow the surface around curves. Because of
this, Rayleigh waves can be used to inspect areas that other waves might have
difficulty reaching.
Fig. 6: Elliptic orbit motion created from surface waves.
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2.4.4
PLATE WAVES.
Plate waves are similar to surface waves except they can only be generated in
materials a few wavelengths thick. There are two (2) types of plate waves- the
lamb waves and the love waves. Lamb waves are the most commonly used plate
waves in NDT. They are complex vibration waves that propagate parallel to the
test surface throughout the thickness of the material. Propagation of Lamb waves
depends on the density and the elastic material properties of a component. They
are also influenced a great deal by the test frequency and material thickness. Lamb
waves are generated at an incident angle in which the parallel component of the
velocity of the wave in the source is equal to the velocity of the wave in the test
material. Lamb waves will travel several meters in steel and so are useful to scan
plate, wire, and tubes.
MODES OF PARTICLE VIBRATION IN LAMB WAVES.
With Lamb waves, a number of modes of particle vibration are possible, but the
two most common are symmetrical and asymmetrical lamb waves. The complex
motion of the particles is similar to the elliptical orbits for surface waves.
Symmetrical Lamb waves move in a symmetrical fashion about the median
plane of the plate. This is sometimes called the extensional mode because the
wave is “stretching and compressing” the plate in the wave motion direction. Wave
motion in the symmetrical mode is most efficiently produced when the exciting
force is parallel to the plate.
The asymmetrical Lamb wave mode is often called the “flexural mode” because
a large portion of the motion moves in a normal direction to the plate, and a little
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motion occurs in the direction parallel to the plate. In this mode, the body of the
plate bends as the two surfaces move in the same direction.
Fig 7: Symmetric and Asymmetric Lamb Waves
As mentioned previously, longitudinal and transverse (shear) waves are most
often used in ultrasonic inspection. However, at surfaces and interfaces, various
types of elliptical or complex vibrations of the particles make other waves
possible. Some of these wave modes such as Rayleigh and Lamb waves are also
useful for ultrasonic inspection.
The table below summarizes many, but not all, of the wave modes possible
in solids.
Wave Types in Solid
Particle Vibrations
Longitudinal
Parallel to wave direction
Transverse (Shear)
Perpendicular to wave direction
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Surface - Rayleigh
Elliptical orbit - symmetrical mode
Plate Wave - Lamb
Component perpendicular to surface
(extensional wave)
Plate Wave - Love
Parallel to plane layer, perpendicular to wave
direction
Stoneley (Leaky Rayleigh
Wave guided along interface
Waves)
Sezawa
Anti-symmetric mode
· Table showing the various wave types in solid.
2.5 CONCLUSION.
It can be concluded that sound can be propagated through air, water and
solid. It can also be seen that when sound is being propagated, its behavior affected
by three (3) things; the relationship between density and pressure, the motion of
the medium and the viscosity of the medium. When sound is propagated, it can
either be reflected, refracted, diffused or diffracted.
Also, in solids, sound waves can be propagated in many modes but the most
common are four (4) modes based on the behavior of the particles. The modes are
longitudinal waves, shear waves, surface waves, and in thin materials, as plate
waves. Some other modes are stoneley and sezawa.
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2.6 REFERENCES.
J.E. Salihu.
“Revised and enlarged edition of Model physics”.
ISBN 978-33991-6-0.
Pg 251-265.
Wiener and Keast. “Experimental study of the propagation of sound.
Journal of the acoustical society of America 31.
Pg. 724.
websites.
v www.Amazon.com/books.
v www.tutorvista.com
v
www.physicsforums.com
v www.acoustics.salford.ac.uk
Google (Propagation of sound and propagation of sound in solid).
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