Fundamentals of Ultrasonic waves and applications

Fundamentals of ultrasonic
Dr. Priyanka Tabhane
Department of Physics,
RTM Nagpur University

Ultrasonic waves
• Vibrational waves of frequency above the hearing range of the
normal ear are referred to as ultrasonic.
• Frequency is more than about 20000 cycles per second.
• In minimum frequency range, length of ultrasonic waves in solid
is about 8 inch, in liquid 2.4 inch, in air 0.63 inch. Frequencies
of 10kHz to 1 MHz are used for industrial applications, sound
ranging, submarine signalling and communication.
• Frequencies 10 kilo hertz to 20000 kilo hertz are used in testing
materials for flaws, chemical treatment, medical therapies etc.
• All frequencies are suitable for investigation of physical
properties of matter.
• Presence of medium is essential for transmission of Ultrasonic
waves.
• Any material that has elasticity can propagate Ultrasonic waves.
Dr Priyanka Tabhane

• Types of waves-
1. Longitudinal waves or Compressional or Pressure Waves.
2. Transverse or shear waves
3. Surface or Rayleigh waves
4. Lamb or Flexural or Plate Waves
Dr Priyanka Tabhane

Longitudinal waves
• When the motion of a particle in a medium is parallel to the
direction of wave propagation longitudinal wave exists
• they are often referred as L waves
• they can travel in liquid, solid & gases and are easily turn treated
and detected
• waves have high velocity of travel in most media
• wavelength in common materials are usually very short in
comparison with the cross section area of transducer that is the
material that produces the wave
• longitudinal wave maybe generated within a medium
by vibration of anyone of its surface in a normal direction at an
ultrasonic frequency
Dr Priyanka Tabhane

Dr Priyanka Tabhane
figure shows longitudinal wave travelling through medium

Shear or transverse waves-
• When shear waves are used, the movement of particles in a
medium is at right angles to the direction of wave
propagation.
• They are referred as S waves
• The wave movement is in the X direction, the particle
displacement is in Y direction.
• These waves can also exist either in Limited area or entirely
throughout a body.
• Beam does not extend to a surface parallel to the direction of
travel
• Have velocity one half of that of L-waves.
• Because of lower velocity wavelength of S waves is much
shorter than L waves
Dr Priyanka Tabhane

• shorter wavelength make them more sensitive to small
inclusions
• Therefore they more easily scattered within the material
• S waves do not travel in liquid or gases since there is little or
no elasticity to shear in such material
• Shear waves are generated by applying a sharing force to the
face of material that is rocking it back and fourth in the
direction parallel to the surface
figure shows particle motion and wave direction of S waves
Dr Priyanka Tabhane

Surface or Rayleigh Waves
• Waves can be propagated over the surface of a path without
penetrating below that surface to any extent.
• These waves are reflected to water waves which travel over
body of water
• Their velocity depends upon the material itself
• Velocity is about nine-tenth of s wave velocity
• They are generated by shaking an area of a surface back and
forth in manner similar that by which S waves are generated
Dr Priyanka Tabhane

• Wavelength is extremely short And the plate on
which it travels is at least several wavelengths thick.
• Surface wave consist of both l and S types of particle
motion
• These waves are used to detect cracks or flaws on or
near the surface of test objects
• Figure 3 surface waves travelling over a plate
Dr Priyanka Tabhane

Lamb or Flexural or Plate Waves
• Produced in thin metal, whose thickness is
comparable to the wavelength of ultrasonic waves.
• Particle motion in them is similar to shear and
surface wave but extends throughout the medium
Dr Priyanka Tabhane

Q.2 Discuss properties of ultrasonic waves.
• Frequency υ
• Velocity v
• Wave length λ
• Energy E
• Mode of propagation
• Transmission of sound waves
• Reflection at boundary
• Angle of reflection and refraction
• Diffraction
Dr Priyanka Tabhane

• Frequency υ –
o All the sound waves oscillate at a specific frequency,
or number of vibrations or cycles per second.
o Human hearing extends to a maximum frequency of 20
kilohertz while the majority of ultrasonic applications
utilised frequency between 20 kHz to 500 MHz.
o At frequencies in the megahertz range sound energy
does not travel efficiently through air or other gases
but it travels freely through most liquids and common
Engineering Materials.
o And hence ultrasonic waves are high frequency waves.
Dr Priyanka Tabhane

• Velocity v-
o The speed of sound waves , varies depending
on the medium through which it is
travelling, affected by medium density ρ and
Elastic properties (Elastic constant E).
o Different types of sound waves will travel at
the different velocities
𝑣 = √
𝐸
𝜌
Dr Priyanka Tabhane

• Wave length λ - any type of wave will have
an associated wavelength, which is the
distance between any two corresponding
points in the wave cycle as it travels through a
medium.
o Wavelength is related to frequency and
velocity by simple equation
𝜆 = 𝑣/υ
o Wavelength is a limiting factor that control the
amount of information that can be derived
from behaviour of wave .
Dr Priyanka Tabhane

• Energy E -
E= h υ
o As frequency of ultrasonic waves is high.
o So, ultrasonic waves are high energetic waves.
Dr Priyanka Tabhane

• Mode of propagation-
o sound waves in solids can exist in various modes
of propagation that are defined by type of
motion involved.
o Longitudinal and shear waves are the most
common mode employed in ultrasonic testing.
o Surface and plate waves are also used on
occasion.
o Sound waves may be converted from one form to
another.
o Most commonly shear waves are generated in a
test material by introducing longitudinal waves at
a selecting angle.
Dr Priyanka Tabhane

• Transmission of sound waves-
o The distance that a wave of a given frequency and
energy will travel depends on the material through
which it is travelling.
o In general, material that are hard and homogeneous
will transmit sound waves more efficiently than that
are soft and heterogeneous or granular.
o Beam spreading, attenuation and scattering will
decide the distance of sound wave in a given
medium.
o As a beam Travels the leading edge becomes wider,
the energy associated with the wave is spread over a
larger area, and eventually the energy dissipitates.
Dr Priyanka Tabhane

o Attenuation is the energy loss associated with the
sound transmission through a medium, essentially
the degree to which energy is absorbed as the wave
front moves forward.
o Scattering is a random reflection of sound energy
from grain boundaries and similar microstructure.
o As frequency goes up, beam spreading increases but
the effect of attenuation and scattering are reduced.
Dr Priyanka Tabhane

• Reflection at boundary-
o When sound energy travelling through a material,
strikes a boundary with another material, portion of
energy will be reflected back and the portion will be
transmitted through.
o The amount of energy reflected or reflection
coefficient, is related to relative acoustic
impedance of the two materials.
o Acoustic impedance is material property defined as
density multiplied by speed of sound in a given
material.
Dr Priyanka Tabhane

o For any two materials, the reflection coefficient as
percentage of incident energy pressure may be calculated
formula
𝑅 =
𝑍2− 𝑍1
𝑍2+𝑍1
where R- reflection coefficient
Z1 - acoustic impedance of first material
Z2- acoustic impedance of second material
o For metal air boundaries, in ultrasonic wave application like
flaw detection, the reflection Coefficient approaches 100%.
o Virtually all the sound energy is reflected from crack or other
discontinuity in the path of the wave.
o This is fundamental principle that makes ultrasonic flaw
detection, detection of any object in sea etc.
Dr Priyanka Tabhane

• Angle of reflection and refraction-
o Sound energy at ultrasonic frequency is highly
directional and sound waves used for flaw detection
in any metal, object detection in sea are well
defined.
o In situation where sound reflects off the boundary,
the angle of reflection equal to angle of incidence.
o Sound beam that hits surface at perpendicular
incidence angle will reflect straight back.
o Sound beam that hit a straight surface at angle will
reflect forward at the same angle.
Dr Priyanka Tabhane

=
Dr Priyanka Tabhane

o Sound energy that is transmitted from one material
to another bends in accordance with Snell's law of
refraction.
o Again a beam that is travelling straight will continue
in a straight direction, but a beam that strikes a
boundary at angle will be bent according to formula
𝑠𝑖𝑛𝜃1
sin 𝜃2
=
𝑣1
𝑣2
θ 1 = incident angle in first material
θ 2 = refracted angle in second material
v1 = sound velocity in first material
v2 = sound velocity in second material
Dr Priyanka Tabhane

• Diffraction –
o Ultrasonic waves do not always propagates in
rectilinear manner. Eg. Wave passing near the edge
of an object has a tendency to become bent towards
or around it. This bending of wave is called
diffraction.
o Ultrasonic signals that would normally be received at
certain point may be diverted by diffraction &
received at some other point.
Dr Priyanka Tabhane

Velocity in fluids
• There are number of different types of velocity that
can be discussed. Most significant are referred to
as phase velocity, group ( bulk) velocity and signal
velocity.
• Phase velocity may be defined as speed with which a
phase is propagated along a wave.
• It refers to a condition existing along a line of
propagation that seems to show a change in
phase travelling along with and superimposed on
the wave itself.
Dr Priyanka Tabhane

• Group velocity is used to indicate the velocity with
which the envelope of a wave is propagated when
the wave is amplitude modulated. Group velocity is
most often considered in ultrasonic work.
• Signal velocity is very complex condition existing only
when a medium is dispersive. In such cases different
signals seems to travel with different velocity and
actual speed of travel of a particular signal is its
signal velocity.
• Velocity of the wave and that of individual particle of
material are not same.
Dr Priyanka Tabhane

• Velocity of sound in liquid is 5 to 10 times the velocity in
its vapour at same temperature, due to close packing of
the molecules in liquid.
• The ultrasonic velocity provide an excellent means of
studying various types of change of phase in vicinity of
melting point of super cooled liquids and round the
critical temperature of individual liquids and mixtures,
transition in liquid crystals from their anisotropic region
to isotropic region.
• The formula by which ultrasonic velocity were calculated
is
u =
2d
t
where, d = Separation between transducer & reflector
t = Traveling time period of ultrasonic wave.
Dr Priyanka Tabhane

• Velocity measurements in fluids shows, associative
or dissociative nature of the molecules.
• If velocity goes on increasing with concentration or
temperature means the chemical bond in the
solution is strong and it thus shows associative
nature of the solution.
• If the velocity goes on decreasing with increase in
concentration or temperature, shows the dissociative
nature or breaking up of molecules in the solution.
Dr Priyanka Tabhane

• Only L waves can transmit in liquid and gases.
• In such cases it can be assumed that the vibration
takes place too rapidly for heat to exchange.
• The velocity in either a liquid or gases is then
𝑣 =
𝐾
𝜌𝐵𝑖𝑠
=
1
𝜌 𝐵𝑎𝑑
Where K- ratio of specific heats
Bis - compressibility at a constant temperature
Bad - adiabatic compressibility.
Dr Priyanka Tabhane

Ultrasonic absorption
• The study of ultrasonic absorption is to understand
how the medium responds to the perturbation and
relaxes when the perturbation passes on.
• Absorption losses are characteristic of the medium
through which the waves travel and the evaluation
can yield the information about the physical
properties of the medium.
• When a plane progressive wave passes through a
system, the amplitude or intensity of a sound wave in
a system decreases with the distance travelled by the
wave, which is called attenuation.
Dr Priyanka Tabhane

• This attenuation arises from deviation of energy from
the plane wave by regular process like reflection,
refraction, diffraction, scattering and absorption of
energy by the medium, when the mechanical energy
is converted into heat by the internal friction.
• The ultrasonic absorption (α/f2, where f = ultrasonic
frequency) in the fluid media are attributed mainly
due to the processes viz.; absorption due to viscosity,
absorption due to thermal (heat) conduction.
Dr Priyanka Tabhane

Absorption due to Viscosity:
• The viscosity (fluids resistance to flow) of a fluid
corresponds to the shear elasticity in a solid.
• If the medium has a finite viscosity, the frictionless losses
of the energy occur.
• This gives to the ultrasonic absorption due to shear or
classical viscosityand is given by,
α
f2
shear
=
8π2
ηs
3ρu3
np. sec2
cm
Where, α = absorption coefficient
f2 = ultrasonic frequency
ηs = coefficient of shear viscosity
ρ = density of the medium
u = ultrasonic velocity
Dr Priyanka Tabhane

Ultrasonic absorption due thermal or heat
conduction:
• Heat conduction (or thermal conduction) is the
movement of heat from one object to another
one that has different temperature when they are
touching each other. For example, we can warm
our hands by touching hot-water bottles. When
the cold hands touch the hot-water bottle, heat
flows from the hotter object (hot-water bottle) to
the colder one (hand). People make things with
different thermal conductivity, for example
cookware to heat things or insulated containers
to keep hot things hot or cold things cold.
Dr Priyanka Tabhane

• The absorption coefficient of material can be
determined by measuring the heating which occurs
as a result of ultrasonic irradiation.
• When narrow focused beams, heat a sample over
the available volume, material restricted to small
dimensions, then the effect of heat conduction to
surrounding unheated regions become significant,
complicating the relation between major
temperature and acoustic parameters.
• The sound energy is also absorbed due to the ability
of thermal conduction of the medium.
Dr Priyanka Tabhane

• The heat energy is conducted from higher
temperature regions to the lower one and so the
compressed region will return lesser work on the
expansion than the work required compressing it.
This gives rise to the absorption of sound energy
(α / f2)thermal as:
α
f2
thermal
=
2π2K γ − 1
ρu3γCT
np. sec2
cm
K = coefficient of thermal conductivity
CT= isothermal heat capacity
γ =ratio of isobaric and isochoric heat capacities
Dr Priyanka Tabhane

Absorption testing-
• Ultrasonic testing has been successfully used in
testing of materials by noting the absorption
pattern.
• Typical pattern is shown in figure.
Dr Priyanka Tabhane

• These results can be correlated to differences in grain
structures or the internal condition of material.
• One successful application has been the testing of
material in plates where the thickness of the plate
was too small to permit ordinary reflective thickness
measurements.
• On a plate that is sound , a series of reflections of
considerable Height and spaced at the proper
distance will be clearly noted.
• when the plate is laminated, reflections entirely
disappear, thus giving a very strong and sharp
indication of defects. the laminated parts can be
located exactly because of directional characteristics
of ultrasonics.
Dr Priyanka Tabhane

Ultrasonic generators
• Sound waves are generated or received by
Transducer, that is any device which converts energy
of one form to that of another.
• In this case transformation of ultrasonic energy to or
from electrical, mechanical or other forms of
energy.
• A reversible transducer is one which will make the
conversion in both direction with equal efficiency.
Dr Priyanka Tabhane

Different types of transducers are classified as
• Piezoelectric oscillator- uses piezoelectric effect -which is
reversible- frequency range extends from 20 kilo hertz to 10
gigahertz
• Magnetostrictive oscillators- magnetostriction effect- reversible- not
used at frequencies higher than 40 kilo Hertz, but range can be
extended without difficulty to over hundred kilo Hertz
• Mechanical transducer- purely mechanical oscillators- whistle
siren- Irreversible- used in high power applications- frequency
beyond 50 kilo Hertz
• Electromagnetic transducers- intensity application at low
frequency given in audible range
• Electrostatic transducers- low intensity with a upper frequency of
200 kilo Hertz
• Miscellaneous transducers- includes thermal chemical and optical
transducer
Dr Priyanka Tabhane

Piezoelectric effect
• In 1880, Curie brothers, J Curie and P Curie, discovered that when a
crystal having 1 or more polar axis or lacking Axis symmetry is
subjected to mechanical stress and potential difference occurs.
• Inverse Piezo electric effect- The opposite effect predicted by
Lippmann in 1881 and verified experimentally by Curie Brothers in
the same year : when an electric field is applied in the direction of
Polar axis causes a mechanical stream in crystal segment. The
amount of strain is is directly proportional To the intensity of
applied electric field
• PEE occurs in several natural and artificial crystals and defined as a
change in the dimensions when an electric charge is supplied to a
crystal faces.
Dr Priyanka Tabhane

• Piezoelectric effect - when an AC voltage is applied across
Piezo Frequency of Crystal, Which is determined by the
physical dimensions and by the way the Crystal is cut.
• the electric crystal, such as Quartz crystal, vibrates at the
frequency of applied voltage.
• Vibrations of maximum amplitude occur at the natural
resonant frequency of the vibration
• Natural resonant frequency of the vibration is given by
𝑓 =
𝑛
2𝐿
𝑌
𝜌
Where L is the length of thickness of the Crystal plate, Y is Young's
modulus along the appropriate direction And 𝜌 is the density of
the Crystal .
Dr Priyanka Tabhane

Dr Priyanka Tabhane
Quartz is very commonly applied for ultrasonic generation. a quartz
crystal is shown in figure with the hexagonal cross sectional normal to the
non polar optical axis denoted by Z axis.
the axes joining opposite edges are designated as x axis and associated
axis which are perpendicular to these and joining opposite faces are
termed as y axis.
X and y axis are polar axis and slab cut with their faces perpendicular to
them manifest the piezoelectric effect
crystal that cut with their faces perpendicular to an x axis and y axis are
termed X cut and Y cut crystal respectively.
the X cut crystals are utilised to propagate compression waves and Y cut
crystal are applied to generate shear waves.

• Piezoelectric crystal can oscillate in either of two mode -
fundamental and overtone.
• Fundamental frequency of a crystal is the lowest frequency at
which it is naturally resonant.
• Because a slab of Crystal cannot be cut too thin without
fracturing, there is an upper limit on the fundamental
frequency.
• For most crystals the upper limit is less than 20 megahertz.
For higher frequencies crystal must be operated in the
overtone mode.
Dr Priyanka Tabhane

Piezoelectric oscillator-
• Ultrasonic wave generator was first designed in 1917 by Langevin.
• It is a triode valve oscillator.
• The plate coil L2 is inductively coupled to grid coil L1.
• When the circuit is switched on the valve starts functioning as oscillator
producing oscillations at frequency given by
𝑓 =
1
2𝜋 𝐿𝐶
Dr Priyanka Tabhane

• The frequency of oscillations can be controlled by varying the
capacitor C.
• The capacitor is varied till the frequency of oscillations of
oscillator matches with natural frequency of the piezo electric
crystal .
• The Crystal subjected to AC voltage produces Ultrasonic waves
in the surrounding air.
Dr Priyanka Tabhane

Measurement techniques
The methods of ultrasonic velocity and absorption may be
categorized as below:
i) Progressive Continuous Wave method
ii) Interferometer method or Standing wave or Resonance
method
iii) Mode conversion or Total Reflection method
iv) Optical method
v) Reverberation technique
vi) Impedance method
vii) Pulse technique
Dr Priyanka Tabhane

Optical diffraction method
• When ultrasonic waves are generated in a liquid in a
rectangular vessel, the wave can be reflected from the walls
of the vessel.
• These reflected waves are called echoes.
• The direct and reflected waves are superimposed, forming
a standing wave.
• The density of the liquid at a node is more than the density at
an antinode.
• Hence, the liquid acts as a diffraction grating to a parallel
beam of light passed through the liquid at right angles to the
wave.
Dr Priyanka Tabhane

• The diffraction grating formed in this way is analogous to a
conventional diffraction grating with lines ruled on a glass
plate.
• The less dense antinodes refract light less and are similar to
the transmitting slits of a conventional grating.
• The denser nodes refract light more and are similar to the
opaque part of a conventional grating.
• optical diffraction method may be used for measurement in
transparent liquids and solids.
• when sound waves pass through a transparent material,
periodic variations takes place in the refractive index, mostly
in regions of compression and minimum in regions of
expansion.
Dr Priyanka Tabhane

• these variations produce optical diffraction grating having a
spacing equal to ultrasonic wavelength.
• When a beam of light, originating from a monochromatic source
( Mercury discharge tube placed behind the suitable filter or
sodium lamp), passing through a narrow slit, is rendered parallel
by placing slit at focal point of converging optical lens.
• A parallel monochromatic beam passes through the medium And
is brought to a focus in the focal plane of microscope.
• In absence of ultrasound only a single image of slit is observed,
but when propagation takes place, several equally spaced parallel
images of the Slit are observed as a result of diffraction.
Dr Priyanka Tabhane

• The distance of separation of neighbouring images can be
measured by means of travelling microscope varies in inverse
proportion to spacing of grating. i.e. wavelength.
• The graticule is calibrated either by means of preliminary
measurement with liquid in which the velocity of sound is
known or by employing optical grating of known spacing. (eg
40 lines per millimetre)
• Velocity of sound is determined by multiplying the measured
value of wavelength by the frequency of source.
Dr Priyanka Tabhane

Dr Priyanka Tabhane
Arrangement for optical diffraction method

Dr Priyanka Tabhane
Stationary wave pattern
Image of sodium slit obtained with
ODM

• The grating element is equal to the wavelength of the
ultrasonic waves, denoted by d.
• If λ is the wavelength of the light passed through the grating
that is diffracted by an angle θ, then the nth order of the
maximum is given by:
d sin θ = n λ
or d= n λ/ sin θ
now, velocity of ultrasonic wave,
v= fd or d=v/f,
v/f= n λ/ sin θ or v= n f λ/ sin θ
Dr Priyanka Tabhane

• Advantage of this method is that velocities can be determined
in comparatively small samples of material.
• Once the system is setup, measurements can be made on
different samples in fairly Rapid succession.
• Sensitivity of method depends on fineness of ultrasonic
grating.
• If the grating is too coarse, the image formed by diffracted
light beams are too close together for proper resolution .
• For liquids the lowest practical frequency is about 10
megahertz for which Quartz crystal source is necessary.
• The method is unsuitable for gases because of the low
degree of contrast in refractive index between compressed
and rarefied regions of wave.
Dr Priyanka Tabhane

Interferometer method or Standing wave or Resonance method
• An acoustic interferometer is an instrument for measuring
the physical characteristics of sound waves in a gas or liquid.
• It may be used to measure velocity, wavelength, absorption,
or impedance.
• In this technique, there is a X-cut quartz crystal in the bottom
of the cell which when excited by external r.f. source having
same frequency as the fundamental frequency of the X-cut
quartz crystal, ultrasonic waves are produced and propagate
towards metallic reflector, which is fitted with a micrometer
(with least count 1 µm) which can be moved up and down in
the sample kept in cell.
• Ultrasonic waves reflected from metallic reflector superpose
with propagating ultrasonic waves and standing wave pattern
is formed. Dr Priyanka Tabhane

• When distance between transmitting crystal at the bottom of
the cell and metallic reflector equals integral multiple of λ/ 2
(λ is the wavelength of the ultrasonic waves), maxima in the
micrometer fitted with interferometer is observed.
• By monitoring known number of maxima in the cell and
noting down corresponding distance reflector is moved, the
wavelength λ of the ultrasonic waves is determined which is
used for the determination of the ultrasound velocity, u (u = n
λ) at a given frequency.
Dr Priyanka Tabhane

Dr Priyanka Tabhane

Pulse Technique
• Technique which utilized pulse ultrasound are the most widely
used for testing materials because the experimental
configuration is simple to design and operate, measurements
are rapid, non-invasive and non-intrusive, there are no
moving parts and the technique can easily be automated.
• This technique was introduced by Pellam and Galt and
Pinkertanin 1946, from the principle of radar.
• This is the most popularly used technique to determine the
velocity and absorption in liquids and solids in the frequency
range of a few MHz to tens of GHz and in gases; the frequency
range of tens of KHz to a few hundreds of MHz
Dr Priyanka Tabhane

• Pulse method consists of generation of short regular pulses of
ultrasonic waves in the test sample, the time taken for them to
pass through a measured distance be measured.
• It is mainly based on the principle that the time required for
the passage of short duration pulses through a sample of
known thickness is measured accurately to determine the
ultrasonic velocity.
• The absorption coefficient () is measured from the height of
different echoes formed due to passage of a short duration
pulse through the sample of known thickness.
• The equation used to determine () is given by:
𝐴 = 𝐴0𝑒−𝛼𝑡
Where A0 & A are the amplitudes or heights of first & second
echo respectively &‘t’ is the time.
Dr Priyanka Tabhane

• More sophisticated pulsed methods have been developed to
improve the accuracy of measurements (e.g., Pulse echo
overlap, sing around, pulse interferometer).
• The simplest and most widely used technique for making
ultrasound technique for making ultrasound measurements is
called pulse-echo technique.
Dr Priyanka Tabhane

Sing-Around Technique:
This method is an automated method for measuring ultrasonic
velocity with high accuracy.
It is very easy to handle, convenient and versatile.
Dr Priyanka Tabhane
Block diagram of Sing-Around Technique

• In this method a trigger transmitter sends an electrical pulse to
the transmitter transducer which generates mechanical waves
in the specimen.
• The pulse waves received by the receiving transducer are
amplified and then used to trigger the transmitter.
• This is pulse transmission device for which short pulses from
transmitter T pass through the material and are picked up by
the receiver R.
• On receipt of each pulse by R activates the pulse generator to
cause another pulse to be transmitted by T.
• The pulse repetition frequency is determined by the time taken
for the pulses to pass through the material by the frequency
counter.
Dr Priyanka Tabhane

• the velocity is determined if the thickness of the sample is
known.
𝑣 = 𝑓𝑇 =
𝑇
𝑡
• This loop runs continuously, the frequency of occurrence is
measured.
• The principle disadvantage of this system is that any change in
amplitude of the selected cycle, results in significant change in
repetition rate.
Dr Priyanka Tabhane

Pulse Echo Overlap (PEO) Technique:
• The PEO method utilizes either rf bursts (to measure phase
velocity) or broad band pulses (for group velocity).
• the PEO method is capable of measuring accurately from any
cycle of one echo to the corresponding cycle of next echo.
• In PEO method overlap of echo is accomplished by visual
observation by the technician performing the measurements.
• The main drawback of this method is that it cannot be
automated as its echoes are overlapped by the observer in
scope time and not in real time.
Dr Priyanka Tabhane

This technique has the following advantages.
• Using this method, ultrasonic velocity and attenuation
measurement can be made simultaneously.
• It can be operate either with the transducer bonded directly
to sample or with buffer rod interposed between them.
• It can be operated by broad band pulses or r.f. burst pulses.
However the broad band pulses are more adequate for proper
overlap and in a non dispersive media.
• It allows the transmitter to operate at a much lower
frequency.
• It can be used to measure the group velocity and phase
velocity.
• It requires minimum two echoes for overlap and so it can be
used for highly absorbing specimen.
• It does not depend upon the shape of the echoes.
Dr Priyanka Tabhane

• The block diagram of PEO technique is shown in Figure.
• At regular intervals, the trigger pulses from a trigger generator
are used to excite the time base of CRO and the pulse
generator simultaneously.
• The time base is connected to the x-plates of a CRO.
Dr Priyanka Tabhane

• The pulse generator generates the short duration modulated
pulses enclosing r.f. signal at desired frequency, and they are
used to excite the transducer at its natural or fundamental
frequency.
• At the same time, the signals (pulses) are also applied to the y-
plates of the CRO through a narrow band amplifier tuned at the
desired frequency.
• The ultrasonic waves generated by the vibration of transducer
are allowed to propagate through the sample under
investigation.
• The waves after traveling through the sample are reflected by
reflector and are received back by the transducer which acts as
a receiver also.
• The received ultrasonic pulses are converted into an electrical
signal, which appears at the y-plates of CRO after amplification
through a tuned amplifier.
Dr Priyanka Tabhane

• The time duration, in which the pulse passes through the sample
and received by the transducer after reflection from the reflector,
the electron beam in CRO will have moved a given distance
towards right and the signal corresponding to received echoes
will be at a lower height than the transmitted one.
• By synchronizing the time base of CRO with the pulse repetition
rate, stationary pulses (echoes) on the screen of CRO can be
obtained.
• The traveling time (t) of the waves through the sample can be
determined from the time base of CRO or a frequency counter
connected with the circuit and by measuring the distance
between transducer and reflector, the ultrasonic velocity can be
calculated by using formula v= fd = d/t
• The attenuation () can be determined by noting the values of
the heights (amplitudes) of the echoes. Thus ultrasonic
absorption (/f2) can be calculated, where, f = frequency of
vibration of the transducer.
Dr Priyanka Tabhane

Fine echo wave train pattern Selection of two echoes Overlapping of
two selected echoes
Fine amplitude pattern for measurement of Attenuation
Dr Priyanka Tabhane

Pulse Echo Techinque
• The pulse generator sends an electric pulse to the
transmitter probe, which produces an ultrasonic pulse.
• This ultrasonic wave spreads into the specimen and is
reflected to the receiver, which transforms the wave
into an electric signal.
• This signal is then send to the amplifier and from there
to the cathode ray (CR) tube, which displays the signal
as peaks.
• The horizontal axis is proportional to the time t.
• The vertical axis shows the amplitude of the signal.
Dr Priyanka Tabhane

• The time base generator produces a high frequency
wave and makes the spot move across the CR tube.
• The first peak on the display represents the generated
ultrasonic pulse.
• The ultrasonic wave travels through the specimen until
it is reflected or scattered by a surface.
• The reflected part of the wave can be seen as peak on
CR tube.
• The other part of the wave continues to the back wall
of the specimen and will be reflected there.
Dr Priyanka Tabhane

Dr Priyanka Tabhane
Images of ultrasonic
probe of 1MHz, 2MHz &
5MHz frequency
Connection Details for Viewing Signal on Oscilloscope

Dr Priyanka Tabhane
Echo pattern on two channel digital storage oscilloscope
Simple Echo pattern

Single Relaxation for internal degrees of freedom
• Relaxation usually means the return of a perturbed system into
equilibrium. Each relaxation process can be categorized by a
relaxation time τ.
• The degrees of freedom refers to the number of ways a molecule
in the gas phase may move, rotate, or vibrate in space.
Dr Priyanka Tabhane

• Sound absorption in fluids is many times larger than that
resulting from classical causes: viscosity and heat conductivity
of fluid.
• The total energy of molecules in a fluid is distributed
partly, among their translational or external degrees of
freedom, and partly among their rotational and vibrational
or internal degrees of freedom.
• Under equilibrium conditions, the distribution of energy
among the various external and internal degrees of freedom
will be that characteristic of their common temperature.
• When the energy of an element of fluid is suddenly increased,
there is not only redistribution of energy among the various
translational degrees of freedom, but also the exchange of
energy between the external and internal degrees of freedom
Dr Priyanka Tabhane

• The relevant time constant characterizing the processes is of
the order of Collision time Tc between the molecule.
• Establishment of thermal equilibrium between the
translational and internal degrees of freedom is in general
much slower, the corresponding time constant on the
relaxation time t being much larger than Tc.
• As a consequence there is a lack of thermal equilibrium
between the two sets of degrees of freedom.
• The consequent irreversible exchange of energy between the
two energy modes give rise to an additional absorption of
sound in fluids, the absorption per wavelength attaining a
maximum value when the period of sound wave is of the
same order of magnitude as relaxation time.
Dr Priyanka Tabhane

Relaxation in binary mixtures
• Consider a mixture of two gases ‘A’ and ‘B’ at pressure ‘P’.
• Let the mole fraction of gas ‘A’ be (1 - x) and that of gas ‘B’ is
‘x’.
• Let specific heat at constant volume of two gases in their
pure state, per gram mole, be (Cv)A and (Cv)B respectively.
• let us assume that, the pure gas ‘A’ at pressure ‘P’ has a single
relaxation time ‘τAA’, internal specific heat CA and the
molecule of gas ‘B’ are spherical i.e. it has no Internal energy.
• In the mixture, molecule ‘A’ can exchange its internal energy
with translational energy of the molecules not only in
collision with another ‘A’ molecule but also in a collision with
‘B’ molecules.
Dr Priyanka Tabhane

• let the relaxation time of single ‘A’ molecule in pure gas of ‘B’
molecules at pressure P be τAB.
• As only the binary collisions are effective, ‘A’ molecules in the
mixture will relax their internal energy at rate characterized
by relaxation time τ11 , such that,
1/τ11 = (1-x)/τAA + x/τAB
• Since of total number of collisions suffered by ‘A’ per
second, a fraction (1-x) are of ‘AA’ collisions and a fraction
(x) are of ‘AB’ collisions.
• Similarly, if the gas ‘B’ is in its pure state is assumed to have a
single relaxation time τBB, internal specific heat CB , while ‘A’
molecule assume to be spherical, the mixture will have
relaxation time τ22
1/τ22 =x /τBB + (1-x)/τBA
where τBA Is define similar to τAB
Dr Priyanka Tabhane

• Finally if both ‘A’ and ‘B’ molecules in the mixture
possess internal energy, the mixture may be regarded as
having two degrees of freedom excited in parallel with
relaxation time τ11 and τ22, provided that, in the ‘AB’
collisions, no exchange of energy occurs between the internal
degrees of freedom of ‘A’ and those of ‘B’.
• the specific heats associated with the relaxation Time τ11 and
τ22 are
C1 = (1-x)CA , C2= xCB
Cv= (1-x)(Cv)A + x (CV)B
Dr Priyanka Tabhane

Dr Priyanka Tabhane
• At low frequencies absorption α angular frequency
• As ω increases absorption increases and rises to a maximum
and then decreases to zero proportionately to ω-1 .
• The velocity curve has a inflation, at ω = ωm.
• Dispersion and absorption due to thermal relaxation are
significant over a wide range on both sides of ωm

Normal and associated liquids
• Attractive interaction between the molecules play a minor
role in liquids.
• These liquids generally called as normal liquids.
• Normal liquids form a majority and in particular many organic
liquids belong to this group.
• These liquids obey certain empirical rules, with regard to
various physical properties such as vapour pressure, viscosity
etc.
• There exist a large minority of liquid which form an
exception.
• These liquids are known as associated liquids, since the
deviations from empirical rules arise from the tendency of
two or more molecules form a group or a larger molecule.
Dr Priyanka Tabhane

• This associativeness is found to be most predominant
amongst polar molecules.
• Different liquids show different degrees of association
depending upon the strength of intermolecular attractive
interaction, temperature etc.
• In weakly associated liquids, we may have association
between just two molecules, eg. acetic acid where the
monomer CH3COOH molecules and dimar (A dimer is an
oligomer consisting of two monomers joined by bonds that
can be either strong or weak, covalent or intermolecular)
(CH3COOH)2 molecule exist simultaneously.
Dr Priyanka Tabhane

• At the other end of the scale are liquids like water, primary
alcohols and viscous liquids like glycerol, where the
association is amongst a large number of molecules so that
long range order exist.
• Distinction between normal and associated liquids is
quantitative rather than qualitative, and a liquid which
behaves with respect to some physical properties like
associated liquid, at room temperature, behave like a normal
liquid at higher temperature, where the thermal energy
would tend to break the links between the molecules.
• The increase magnitude of the speed of sound in the liquid
state relative to that in vapour state is largely due to the
close packing of molecules in liquid.
• It is of the same order of magnitude in both normal and
associated liquid.
Dr Priyanka Tabhane

Dr Priyanka Tabhane
• We know that, Ultrasonic absorption in liquids is due to their
viscosity and thermal conductivity, and due to thermal
relaxation between translational and internal degrees of
freedom.
• the classical causes and the internal thermal relaxation in
normal liquids explains the sound absorption and dispersion.
• in associated liquid, existence of other relaxation processes has
to be assumed.
• since the coefficient of volume expansion of water is zero at 4oC
and hence attenuation due to internal thermal
relaxation vanishes at this temperature yet the observed
attenuation is about 3 times the classical value throughout the
temperature range 0oC to 90oC.
• example; in weakly associating liquid such as acetic acid in
equilibrium their exist certain number of monomer molecules
and short number of dimer molecule.

Dr Priyanka Tabhane
• temperature and pressure changes associated with the sound
wave will perturb this equilibrium.
• since the equilibrium is restored at a finite rate a typical
relaxation process is expected.
• similarly the equilibrium long range order existing among the
molecules in a highly associated liquid by the sound waves and
the tendency of the system to come to equilibrium will give
rise to sound absorption.
• In highly viscous liquids like glycerol existence of large
relaxation times has to be assumed to explain absorption and
dispersion.
• highly associated liquids will have different properties from
normal liquids.

Dr Priyanka Tabhane
• In liquids the sound wave may perturb the
equilibrium between
i ) the internal and transnational degree of freedom
ii) isomeric forms of molecules
iii)monomers and dimers in weakly associated liquids or
between polymers in associated liquids
iv) Equilibrium degree of long range order in highly associated
liquids.
• In normal liquids, where the molecules can be considered as
having a negligible attractive interaction between them, it is
only temperature, and not pressure difference, associated
with the sound wave cause a lack of equilibrium between the
internal and external degrees of freedom.

Dr Priyanka Tabhane
• i.e. in normal liquids, isothermal pressure or volume change
could not give rise to relaxation effect unless there exist the
small viscous effect.
• In contrast the processes ii), iii), iv) involves changes in
structure either of an individual molecule or of group
molecules .
• If these structural changes involves a change in volume, then
in general both the temperature and pressure fluctuations can
induce lack of equilibrium.

Application of ultrasound
Dr Priyanka Tabhane

Ultrasonic flaw detection
• Flaw detection is the oldest and most common industrial
application of ultrasound.
• Since 1940 the laws of physics that govern the propagation of
sound waves through solid material have been used to detect
hidden cracks, voids, porosity and other discontinuities in
metals, composite, plastic and ceramics.
• High energy sound waves reflect from flaws in predictable
way, producing distinctive echo patterns that can be
displayed and recorded by portable instruments.
• Ultrasonic testing is completely non destructive and safe and
it is a well established test method in many basic
manufacturing processes and services industry especially
involving welds and structural metals.
• Pulse echo method is used for flow detection.
•
Dr Priyanka Tabhane

• The sound energy is introduced and propagate through the material in the
form of waves.
• when there is discontinuity such as a crack in a wave path, part of the
energy will be reflected back from the flaw surface.
• the reflected wave signal is transformed into electrical signal by the
transducer and is displayed on the screen. knowing the velocity of the
wave, travel time can be directly related to the distance that the signal
travel.
Dr Priyanka Tabhane

Signaling
• Since the frequency of the ultrasonic can be made very high
so that wavelength is reduced to small value.
• There for ultrasonic can be transmitted in the form of narrow
beam of small amplitude and large energy
• The ship captain uses ultrasound next to steer it's path it m
when life fails within few metres.
Dr Priyanka Tabhane

Sonar
• Ultrasonic waves sent by the ultrasonic transmitter towards
the target through water and are received by the receiver
lower into the sea water from the ship.
• Doing the time interval between sending and receiving of
ultrasonic we can find the position of target aur submarine.
• We can also find the direction and the velocity of the moving
submarine with these apparatus.
• Sona is used for the detection of enemy submarines inside
water during what time in a senior manual as a retar is used
to trace the enemy airplanes in the atmosphere
• Sonar is used for detecting the glaciers icebergs, sea rocks
and other submerge object
•
Dr Priyanka Tabhane

Cavitation
• When a sound waves travels through a liquid, during the positive of cycle
of wave, the liquid is compressed and during the negative cycle it expands
• When the acoustic pressure is greater than the hydrostatic pressure, voids
are created.
• These voids expand during the negative half cycle and collapse abruptly.
• It places energy, it releases energy, giving rise to shock waves.
• The local temperature rises to 10 hundred and thousands degrees for
very short periods at the frequency of wave propagation.
• This is called cavitation.
• The cavitation process is used in imulsification of two immiscible liquids.
• In the food industry, this method is used in preparation of dairy products
sources gravis salad creams and synthetic creams
• It is used in extraction of hops in brewing industries.
• The sterilisation of milk and tendering of meat by breaking down its fibres
are some other applications.
Dr Priyanka Tabhane

Ultrasonic cleaning
• In the process both agitation and cavitation are involved
• The cleaning of large components is carried out at low
frequency range from 18 kilo h to 40 khz, here cavitation is
most active
• For delegate articles, higher frequency range 100 kilowatt
and one megahertz is used where cavitation is almost absent
• The process is used in removal of grease from engine
components, oil, dust , buffering compounds etc from printed
circuit boards jewellery and various instruments and devices.
Dr Priyanka Tabhane

Acoustical holography
• The waves used in the reconstruction does not have to be the
original, and this allows the use of ultrasonic waves and
subsequent reconstruction of the image using light from a laser.
• But size of image changes in proportion to the ratio of wavelength
of reconstructing wave to the wavelength of the original eliminating
waves.
• There are number of methods of making a political holograms
• One of the method is liquid levitation, where the acoustic waves
from the below the surface of liquids forms an ultrasonic image at
the surface of the liquid that can be rendered visible on
photographic plate.
• The reference been on to the surface or by generating a separate
wave through a second transducer.
• The height of bulge of the liquid surface due to the impetus of an
acoustic wave is critical, it should be small as compared to the
wavelength of the light.
Dr Priyanka Tabhane

Medical applications
• Ultrasound technique have replaced x-rays in almost all areas of medical
diagnostic
• Prenatal corrective surgery has been made possible by the ultrasound
studies in vivo babies
• Ultrasound as many applications in the field of medical diagnostics
• It is particularly well known for is used in the following areas
• Pregnancy and gynaecological problems
• Kidney examination( kidney stones can be pulverised by ultrasound and
then flushed out of the system)
• Examination of scrotum, testes etc
• Examination of thyroid, gullets, larynx and allied organs
• Craniotomy or the study of cranium layer by layer by a safe non invasive
method
A craniotomy is a surgical procedure in which a part of the skull is temporarily removed to expose the brain and
perform an intracranial procedure
Dr Priyanka Tabhane

Fundamentals of Ultrasonic waves and applications

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