This document discusses acoustic transducers and acoustic wave propagation. It begins by defining transducers as devices that convert one form of energy to another, mainly concerning acoustic to electrical and vice versa. It describes how acoustic waves are pressure waves that require a medium, unlike electromagnetic waves. Key points covered include how acoustic waves propagate through air, liquids and solids; properties of piezoelectric materials used in transducers; operation of microphones and speakers; use of transducers for ultrasound and sonar applications; and considerations for transducer design like impedance matching and use of backing materials.

1. Acoustic Transducers
• Transducers are devices that convert energy of one form
to another.
• In acoustics we are mainly concerned with conversion of
acoustic energy to electrical energy or
electrical energy to acoustic energy

2. Acoustic waves
• Acoustic waves are pressure waves.
• They are different from Electromagnetic (EM) waves in
that they need a medium to propagate.
• The waves propagate by induced vibrations in the
medium.
• Therefore acoustic waves do not propagate in a vacuum
unlike EM waves.

3. Acoustic wave propagation in air
• Acoustic waves propagate in air when microscopically
induced oscillations in air particles pass on their energy
to neighbouring air particles which in turn will induce
microscopic oscillations in their neighbouring air
particles.
• The direction of wave propagation is in the direction of
particle motion by the pressure increasing and
decreasing in turn.
Particle
Oscillation
air particles
Fig 1.
Pressure Wave

4. • This type of pressure wave is called a compressional
wave where the direction of wave propagation is normal
to the pressure surface.
• There is weak bonding between adjacent air particles so
no wave is coupled in the plane of the pressure wave
(which takes place when the bonding between particles
are strong as in a solid).
• The speed of sound in air is 343 m/s
• Audible Frequency Range 20 Hz to 20 kHz

5. •The human ear is the most sophisticated acoustic or sound
wave receiver.
•It is tuned to receive sound waves between 20Hz and 20kHz
•Is a frequency filter with bandwidth 20Hz – 20kHz.

6. Condenser Microphone
The capacitance of the parallel plate membrane structure is
given by
When the spacing changes, the charge changes, giving an electric
current through the resistor R.
The voltage measured across the resistor is an electrical image of
the sound pressure which moves the membrane.

8. Speakers
A speaker converts electrical signals into acoustical
energy or sound.
By moving back and forth, the speaker increases and
decreases the air pressure in front of it thus creating
sound waves.
The Essentials are: Cone, Suspension, Magnet, Voice Coil, and Frame.

9. The cone is the main moving mass of the speaker. The
larger the cone, the more mass and surface area a speaker
will have.
The more surface area a speaker has, the more air it can
move. The more air it can move, the louder the speaker can
get.
Accurate, High frequency replication requires smaller
specialty drivers called tweeters.

10. • Generally, Microphones and Speakers have directional
radiation patterns

11. Acoustic waves in Water/Liquid
• Applications: Sonar and Hydrophones (2kHz to 500kHz),
Medical Ultrasonic Scanners (1 to 2MHz).
• There is weak bonding between water molecules therefore
sound propagation is similar to that in air
ie: only compressional waves propagate.
• Sound speed in water is 1482 m/s (normally taken as 1500
m/s) and dependent on the temperature of the water and
salinity.

13. Acoustic waves in solids:
• Applications:
Non Destructive Testing [NDT] (0.5 to 15MHz) – testing for
cracks and fatigue in materials,
High Intensity [18 to 45MHz] – Ultrasonic drilling and
welding.
• Acoustic waves in solids are called elastic waves.
• There is strong bonding between adjacent solid atoms so
waves are coupled in the plane of the pressure wave
• There are three types of elastic waves in a solid
a) compressional (also called longitudinal),
b) shear (also called transverse) and
c) surface waves (also called Rayleigh waves).

14. • The speed of elastic waves depends on the material.
• Compressional wave speed in
Al ~ 6190 m/s, s.steel ~ 5810 m/s, Perspex ~ 2730 m/s
• Shear wave speeds are slightly higher than half the
compressional wave speed.
• Rayleigh wave speeds are about 90% of the shear wave
speeds.

15. Elasticity: Stress and Strain
• When a material is stressed there is an associated deformation
or elongation of the material.
z
y
x
z
y
T3
T3
x
y
T3
T3 x
z
T4
T4
Extensional stress
In z direction
Compressional stress
In z direction
Shear stress
About x direction

16. Elasticity: Stress and Strain
• The elongation per unit length is called strain.
• If we call ξ, η and ζ the elongation in the x, y and z
directions the
Extensional/compressional strains are given by
∂ξ/∂x, ∂η/∂y and ∂ ζ /∂z
Shear strains are given by
∂ζ/∂y + ∂η/∂z in the x direction
∂ζ/∂x + ∂ξ/∂z in the y direction
∂ξ/∂y + ∂η/∂x in the z direction

17. • The relationship between stress and strain are given by
Hooke’s Law, (T is stress and S strain),
Ti = ∑cijSj and Sj = ∑sijTi
where cij are the stiffness and sijthe compliance constants
and both are tensors.
• In general there are 36 cij and sjiindependent constants
( i, j = 1…6).
• The number of independent constants are reduced by
crystal symmetry.

18. Piezoelectricity
• Most acoustic transducers for underwater and NDT
applications are based on excitation of materials that possess a
property called Piezoelectricity.
• The active element in the transducer is piezoelectric.
• Piezoelectricity: Certain crystalline materials
a) generate electric charge under mechanical stress
(this is called the direct effect) and
b) experience mechanical strain or deformation in
the presence of an electric field
(this is called the reverse or converse effect).

19. • Natural materials such as Quartz, and Tourmaline
exhibit piezoelectricity.
• Ceramics such as BaTiO3, PbZrTiO3, PbNb2O6 exhibit
piezoelectricity.
• These possess the ABO3 Pervoskite crystalline structure
• For any material to exhibit piezoelectricity the
microscopic structure must not have a center of
symmetry.

20. Crystal Classes

21. • Common materials found in piezoelectric transducers are :
PbZrTiO3 –Lead Zirconate Titanate or PZT and
PbNb2
O6
– Lead Metaniobate or PMN.
• In transducers these ceramics (PZT, PMN) are made into
discs, cylinders and other useful shapes.
• Discs and cylinders are the most common.
• Electrodes are applied to opposite faces of the discs or
cylinders as shown in the figure.
Ceramic
Ceramic
Disc Cylinder
Electrodes

22. • The crystalline material in its normal form is not
piezoelectric because of the random orientation of the
electric polarization vectors of the domains.
• But when the material is heated above its Curie
temperature (which depends on the material) and a
strong DC electric field applied, the random distribution
of the polarization vectors can be aligned in the direction
of the applied DC field, as shown in the figure below.
• The process of applying the strong DC field at above
Curie temperature and aligning the polarization vectors
is called poling.
• After the alignment of the polarization (and cooling and
removing the DC field) the material is piezoelectric.
Heat above
CurieTemp +
DC
field
-
+

23. • When the material is piezoelectric the application of a stress
T produces not only a mechanical strain S but also an
electric polarization (written in terms of the electric
displacement D)
Dij
= ∑ dij
Ti where i = 1,2,3 and j = 1…6 - direct effect
• In the converse effect the application of an electric field
not only causes a polarization (or D) but also a mechanical
strain
Sj
= ∑ dij
T
Eiwhere i = 1,2,3 and j = 1….6

24. •dij
are the piezoelectric coefficients (where there are 18 in
general)
•Crystalline symmetry reduce the number of independent d
coefficients
•The matrix dij
is symmetric, dij
= dji
.

25. • The complete piezoelectric equations in simple
form are
D = d T + ε E – direct effect
S = sE
T + dT
E – converse effect
where dT
is the transpose of d and
ε the dielectric constant of the material.

26. Transducers
• For many types of piezoelectric transducers the
piezoelectric element is operated in the thickness mode.
• The thickness mode is when the application of an electric
field or stress incident on the piezoelectric element (disc)
makes the element vibrate in the thickness direction
alternately the element expanding and contracting.
• The two extremes of the thickness mode vibration is
shown in the figure.
• If t is the thickness of the disc, the frequency of vibration is
determined by
t = λ /2
where λ is the wavelength = vc /f where vc is the speed of
compressional waves in the piezoelectric material and f is
frequency.
t
Video

27. Discs
Rings
Cylinders

28. Reflection and Transmission of sound waves
• Acoustic impedance of a material is given by
Za = ρvc
where ρ is density (kg/m3
) and
vc the velocity (m/s) of compressional waves in the medium.
• For two media in contact and for normal incidence with sound
wave traveling from medium 1 to 2 the reflection coefficient R at the
boundary is given by
R = (Za2 – Za1)/(Za2 + Za1)
= (ρ2vc2 – ρ1vc1)/(ρ2vc2+ρ1vc1)
and the transmission coefficient T
T = 2 Za2/(Za2+Za1)
= 2 ρ2vc2/(ρ2vc2+ρ1vc1)
• So if Za2 = Za1, the sound wave will be completely
transmitted without any reflection.
inc
R
T
(1) Za1=ρ1vc1
(2) Za2=ρ2vc2

29. • When the piezoelectric disc vibrates there will be
pressure waves generated at the boundary with the
electrode faces.
• If the disc is in air, then R>>T and most of the generated
acoustic energy will be within the disc.
• If the disc is in water, R is reduced and T increased and
the acoustic energy will be transmitted quite easily to
water as Zwater >> Zair.
• If we immerse the piezoelectric disc in water and apply a
continuous wave (CW) electrical signal at the frequency
corresponding to t = λ/2 the output pressure will also be
a CW signal as shown in the figure below,
P
V
V
t
P
t
WATER
P

30. • If the piezoelectric disc is driven by an impulse input
electric signal, after the initial elongation to one of the
extreme position the vibrations will be purely
mechanical oscillations and the output will be
• This is called ‘ringing’ of the piezoelectric element.
• The resultant output pressure is a long pulse- train
waveform.
• Therefore resolution for target detection is very poor.
• To improve resolution we have to shorten the length of
the acoustic pulse-train waveform.
Input
V
Output
P
t
t
P
V
P
WATER

31. Electrical Characteristics of the piezoelectric disc
• The electrical input impedance across the electrical input terminals
is as shown in the figure.
• The frequency at which │Z│ is a minimum is the resonance
frequency fr
.
• The frequency just after fr
at which │Z│becomes large before falling
off is the anti-resonant frequency fp
.
• The equivalent circuit that describe the input impedance is given by
the network shown.
• C2
is the static capacitance of the piezoelectric disc and describe Z
away from resonance.
• The behavior of Z at resonance is described by the C1
LR series
network.
• From the equivalent circuit fr
= 1/[2π√(LC1
)] and fp
= 1/[2π√(LC)]
where C = C1
C2
/(C1
+C2
)
Frequency
Electrical
Input
Impedance
│Z│
fr
fp
C2
L
R
C1

32. • The ringing pressure waveform described above is not in general
very useful because of the long pulse-train.
• To improve resolution it is necessary to shorten the length of the
pulse-train to a few cycles in pulse length.
• This is achieved by fabricating a backing to the piezoelectric disc, as
shown in the figure.
• The backing will increase the T from one face of the disc and
shorten the pulse-train waveform of the output.
• If the Za
of the backing is close to the Za
of the piezoelectric element a
short pulse wavetrain of a few cycles can be obtained as shown, for
an impulse electric input.
• The input electric impedance will be affected by the backing,
damping out the sharpness of the resonance and anti-resonance
frequency peaks as shown in the figure.
Backing
Out put
Pressure
t
t
Electrical
Input
Impedanc
e
fr
fp

33. • The backing material should disperse the acoustic
energy transmitted to it and ensure none of this energy is
returned back to the piezoelectric element.
• This is done by fabricating the backing with a particulate
material, such as tungsten carbide (TC) powder mixed
with an epoxy resin.
• The TC/epoxy mix either pressed on to the disc and
allowed to set or the disc is glued to the TC/epoxy mix
that is already set with a very thin layer of epoxy.
• The backing is also shaped into a V shape at the rear as
shown by the thick dashed line in the figure to disperse
the acoustic energy incident on to it.
• The piezoelectric with the backing is the Transducer and
can be operated both as a Transmitter (converse effect)
and Receiver (direct effect)
Backing

34. • Since acoustic energy is transmitted to the backing the
vibrations of the piezoelectric disc are damped and
consequently the amplitude of the output pressure is
reduced.
• Thus although we get an improvement in resolution by
the shorter pulse length the sensitivity of the transducer
will be affected due to loss in pressure amplitude.
• So a compromise has to be made between resolution and
sensitivity.

35. Immersion Testing
• When the transducer is operating
in a pulsed mode it is possible to
use the same transducer as
transmitter and receiver.
• The time difference between the
incident ( the pulse generated
when the electrical impulse is
applied to the transducer) and
reflected pulse from a surface can
be used to determine the distance
from the transducer to the
reflecting surface.
• The distance from the transducer
to the reflecting surface d is given
by
d= (T/2) * vw
where vw is the sound speed in
water.
d
Tx/Rx
t
V
Reflected
T
Initial

36. • If there is an obstacle in between
the transducer and the reflecting
surface there will be a reflection
from the top of the obstacle
followed by the reflection from
the flat surface (and signals
intermediate between the two
pulses which will contain
information about the character
of the obstacle).
• If there was no reflecting surface
we would only get reflections
and scattering from the obstacle
alone.
t
V
Reflected
signals
top of
target
flat surface

37. • These pulse trains can be analyzed by a variety of
techniques in the time and frequency domains to obtain
information about the characteristics of the obstacle
(target).
• This is the basic principle used in SONAR (2kHz to
500kHz), for target identification and also in medical
applications to obtain echo-graphs in medical ultrasonic
scanners (1 to 2MHz).

38. • Immersion testing can also be used to find defects in
solids as illustrated in the figure.
t
V
Reflected
signals
defect
water
Top
surface
defect
Bottom
surface

39. Hydrophones
• Hydrophones are devices complimentary to
microphones in air.
• These are also transducers but are generally used only in
converting acoustic to electrical signals (SONAR
receptors).
• These are generally used only as listening devices
underwater and find numerous applications such as
submarine, fish detection, sea floor mapping.
• To have a wide angle of reception from any directions
hydrophones are normally made from cylindrical
piezoelectric elements.

40. Some Applications
• Transducers based on a piezoelectric disc
element radiates and receives acoustic
waves from one face of the disc.
• Thus the output/input of these
transducers are directional with limited
beamwidths.
• These transducers are not useful as
widebeam receivers.
• For receiving over a wide range of angles
cylindrical transducers can be used and
are generally the basis of hydrophones as
shown in the figure.
Cable
Cylindrical
element

41. • Transmission of a signal and receiving the echo (pulse-echo mode)
is used in the depth profiling of the seabed.
• Single transducers are used for depth profiling and transducer
arrays are used in sea floor mapping (sidescan sonar).
• The transducer arrays can scan a large area and obtain more
information by sweeping the beam by changing the phase of the
input signal to each element of the array (phased array).
• This type of array transducers are also used in ultrasonic scanning
in medicine.
Input
(V,0) (V,φ)
(V,2φ)
Beam for φ = 0
Beam for φ ≠ 0
depth
sidescan
sonar
sea floor

42. Reflection and refraction at a water/solid boundary
• The reflection and refraction at a boundary
between two media are governed by Snell’s Laws.
• A compressional wave in water (1) incident on a
solid is shown in the figure.
• The compressional wave is refracted with an angle
given by
sin i / sin rc = vc1/ vc2
• The shear wave is refracted with an angle given by
sin i / sin rs = vc1/vs2
where vc1 is the compressional wave speed in
water, and vc2 and vs2 are the compressional and
shear wave speeds in the solid.
• Note that if medium 1 was also a solid that there
would be a reflected shear wave as well.
ii1water
2
solid
vc1
vc1
rc
rs
vc2
vs2

43. Application in ultrasonic inspection (NDT):
• In ultrasonic inspection the presence of two wave types with
different velocities in the material under test will give confusing
results.
• So the angle of incidence is adjusted to be greater than the critical
angle i’ for compressional wave refraction , allowing only the
refracted shear wave to be transmitted.
• Critical angle for compressional wave refraction is
i’ = sin-1
( vc1 / vc2)
• This is accomplished by mounting the transducer on a shoe as
shown in the figure.
• The resultant structure is called an angled probe.
shear
absorbing
medium
perspex
i
i > i’

44. • If it is required to generate a surface wave, the angle of incidence
should be adjusted to a second critical angle i’’ to give a Rayleigh
(surface) wave at a refracted angle of 90º
i’’ = sin-1
(vc1/vs2)
• Inspection of butt welds in parallel sided plates: If there is any
defect in the weld zone, this will cause a reduction in received
signal strength. Distance AB is known as the skip distance. In
practice both probes are mounted on a jig (frame) so that they are
always at the correct separation distance.
• Reflection method for defect detection Surface wave probe
A B
defect
defect