Module – 5

ACOUSTICS
Acoustics is a branch of Physics which deals with the
production, transmission and reception of sound energy in the form of
pressure waves in different Medias.
Classification of sound
1) Based on the frequency range, the sound waves are classified in to 3
classes,
Infrasonic Range Sonic/Audible Range Ultrasonic’s Range
 Frequency below  Frequency between  Frequency grater than
20Hz 20Hz -20 kHz 20kHz
 Cannot be sense by  It can be sense by  Cannot be sense by
human ear human ear human ear
10
The Elastic sound waves with frequency greater than 10 Hz are called
hypersonic waves.

2) Based on frequency spectrum, The audible sound is classified into 2

classes,
Musical sound Noises
 Produce pleasing sensation to ear  Produce irritation and stress to ear
 Musical sounds are periodic  Noises are non periodic vibrations
vibrations
 Sudden changes in the amplitude  It undergoes sudden changes in
do not occur the amplitude and frequency
 It has line spectrum consisting  It consists of complex Spectrum
multiple frequencies of Frequencies

Characteristics of musical sound

 Pitch or frequency
Pitch is a subjective sensation perceived by a listener, when a tone
of a given frequency is sounded. Pitch of a note is a psychological
quantity. Which is only a sensation experienced by the listener.
Whereas, frequency of sound is a physical quantity, which can be
measured accurately. Audible sound is ranges from 20Hz to 20 kHz.
Greater the frequency of musical note, higher is the pitch and vice versa.
 Quality or Timbre
Timbre is the measure of subjective sensation, which enables
a listener to distinguish between the same note played on different
instruments or sung by different singers.
 Intensity of Sound (I)
It is defined as the average rate of flow of sound energy
through a unit area normal to the direction of propagation of sound
waves.
I = 2π2a2η2ρc c
ie, I α a2

Where, a- Amplitude of the wave

η - Frequency of the wave
ρc - Density of the medium
c - Velocity of sound in the media
The SI unit of sound intensity is Watt/ Meter square (W/m 2)

 Threshold Minimum Intensity (I 0)

Human ear have wide range of sensitivity. The minimum
sound intensity that the human ear can perceive is known as threshold
minimum intensity.
The threshold minimum intensity for sound wave of
frequency 1000 Hz is 60 dB or 10 -12 W/m2

 Sound Intensity Level (SIL)

` SIL is the ratio of actual intensity (I) to the Threshold
intensity of sound (I0).
SIL=10 log (I/I0) dB

 Threshold Pain Intensity

The sound intensity at which an individual starts to feel pain
at different pressure level of the medium for same frequency of sound is
called Threshold pain intensity. It is different for different individuals.
Usually intensity level more than 120 dB creates pain to an individual.
60 dB to 120 dB (10 -12 W/m2 to 1 W/m2) is the comfort range for
human at the frequency of 1000 Hertz.
 Loudness of Sound (L)
Loudness is the characteristic of sound by virtue of which we
distinguish 2 sounds of same frequency. In other words, it is the degree
of sensation produced by the human ear.
The loudness of sound wave varies from one listener to the other. Hence
it is known as a psychological quantity.
L α log (I)
Unit of loudness is ‘Phon’.
 Absorption Coefficient (a)
All the materials absorb certain amount of sound energy and
the degree of absorption is different for different materials. Absorption
coefficient is defined as the ratio of sound energy absorbed by the
surface to that of total sound energy incident on its surface.

sound energy absorbed by the surface

𝐀𝐛𝐬𝐨𝐫𝐩𝐭𝐢𝐨𝐧 𝐜𝐨𝐞𝐟𝐟𝐢𝐜𝐢𝐞𝐧𝐭, (𝒂) =
Total sound energy incident on its surface

The unit of Absorption Coefficient is Sabine or Open Window Unit (OWU)

 Reverberation
The phenomenon of persistence of audible sound due to the
multiple reflections from the ceiling, floor, walls and other material
objects in the room, even after the source of sound is switched off is
called reverberation.
 Reverberation Time
It is defined as the time taken for the sound to decrease below
the minimum audibility range (60 dB), from the instant when the source
of sound is stopped. It depends on,
1. Total absorption by the objects in the room.
2. Intensity of sound.
3. Volume of the room.
4. Frequency of sound waves.
 Significance of Reverberation
1. In a sound reflective room, it will take longer time for the sound to die
away and the room is said to be ‘acoustically live’.
2. In a sound absorbing room, the sound will die away quickly and the
room will be described as ‘acoustically dead’.
3. In a room with long reverberation time for sound, create difficulty to
the audience to understand the words of speech.
4. Rooms that are good for both speech and music, typically have
reverberation time between 1. 5 to 2 seconds.
5. A room with more reverberation time is desirable for music.

Sabine’s formulae
Sabine derived an expression for obtaining reverberation time
‘T’ of an Auditorium. Consider a source of sound in a room of volume
‘V’ and sound energy spread out uniformly throughout the hall. Thus the
sound waves get reflected and absorbed by the ceiling, floor, wall and
other objects in the room after multiple reflection. The energy density
become uniform throughout the volume of the room and it become
diffused within the room.
Assume the sound source is stopped at T=0 sec; after T seconds, the
intensity of sound reduced 10 - 6 times of its maximum intensity.
0.163 𝑉 0.163 𝑉
Expression for reverberation T= = is known as
𝐴 𝑎𝑆
Sabine’s formula.
Where, A- Total absorption
V- Volume of the room
a 1,a2,a3…- Absorption coefficient of surfaces S 1,
S2, S3 etc.
Reverberation time ‘T’ is directly proportional to the Volume ‘V’
and inversely proportional to total absorption ‘A’.

Factors Affecting the Acoustics of a Building

An acoustically good hall means that, the one in which every
syllable or musical note reaches to the listener sitting at every point in
the hall with good quality and loudness.
The factors affecting the acoustic behavior of a building are as
follows,
1.Echoes
When the direct and reflected sound waves of a syllable
1
coming to the listener with the time interval about 7 seconds, produces
1
Echoes. The reflected sound arriving earlier than 7 seconds raises
loudness, while those sound waves arriving later produce Echoes.
Echoes create confusion to the listener.
Remedy to control Echo:
Echoes can be avoided by covering the long distant walls and
high ceilings with sound absorbing materials like curtains, absorbent
walls with irregular surfaces etc.

2.Resonance Effect
Sometimes window doors, wooden portions, enclosed air in
the hall or any other flexible objects inside the room get vibrates
according to the frequency of some musical note. When the frequency of
vibration is equal to the frequency original note, produces resonance.
Hence certain tones of the original music will be interfering with the
vibrating sound and get distorted. Thus the intensity of the note is
entirely different from the original one. This is known as resonance
effect.
Remedy to control Echo:
` It can be controlled by fixing the flexible materials suitably
for damping resonant vibrations.

3.Excessive Reverberation
Reverberation produced by the multiple reflections of the
sound waves by the floor, wall, ceiling etc., even after the source of
sound is stopped.
Remedy to control Reverberation:
i) Providing windows and ventilations which can be opened and
closed to reduce the reverberation time to the optimum level.
ii) Decorating the walls with pictures and maps.
iii) Using heavy curtains with folds.
iv) Walls are lined with sound absorbent materials.
v) Having full audience.
vi) Covering floor with carpets and acoustic tiles
4.Focusing Due to Spherical or Curved Region
Due to the architectural designs, a hall may have concave,
spherical or cylindrical portions. The sound after reflection from these
curves, concentrate at its focal point. Hence intensity of sound is high at
that region compared with the other portions. This defect is called
focusing due to curved region.
Remedy to control focusing problem:
i) There should not have curved surfaces. If there is curved region, it
should be covered with sound absorbing materials.
ii) Ceiling height should be low.

5.Echelon Effect
When the sound is reflected by, staircases, ceilings, steps or
any other regular spacing of reflecting surfaces causes reflection of
sound at different time. This produces an interference effect with the
maximum intensity at some point and minimum intensity at some other
points in the hall. This defect is called Echelon effect
Remedy to control Echelon Effect:
i) Covering the steps or regular reflecting spaces by sound absorbing
material such as carpets.
ii) The staircases should be replaced with ramps

6.Extraneous noises
Noises may be defined as the unwanted sound disturbing the
audiences in the room. Generally there are two kinds of extraneous
Noises namely Airborne and structure borne noises.
Air borne
The noise which reaches the hall from outside through open
Windows, doors, ventilations etc. is known as airborne noise.
Remedy:
This may be reduced by providing ventilations with sound
absorbing materials. Or by making the room air conditioned with sound
proof.

Structure Borne
The noises which created within the hall/room by fan, water
tap etc is called structure Borne noises.
Remedy:
This can be reduced by properly oiling and providing bearing
to the fan.
Characteristics of Acoustically Good Building
The branch of science which deals with the planning of
building or an Auditorium with the best audibility of sound to the
audience is called acoustics of building. A good Auditorium must have
the following properties
i) Sound produced at one point must be audible and well heard at all
points without echoes.
ii) The sound should be enough loud, when heard from any point in the
hall.
iii) Continuous sounds of speech must be distinctly heard without
overlapping.
iv) Quality of sound should be same or un-altered.
v) The reverberation time should be proper, ie, the reverberation time
should be from 1 second to 1. 5 second for speech and 1.5 to 2
second for music.
vi) There should not be focusing and interference of sound waves in any
part of the hall.
vii) The boundaries should be sufficiently sound proof to exclude
extraneous noises.
viii) There should not be echelon effect and resonance within the
building.
ix) To maintain adequate loudness using a large sounding board behind
the speakers facing the audience.
 ULTRASONIC’S
The sound waves whose frequency greater than 20 kHz are
called ultrasonic’s or supersonics. It is in-audible to human ear.

Ultrasonic waves having small wavelength and exhibit some

unique properties in addition to the general properties of audible sound
waves.
Properties of Ultrasonic Waves
1. They are highly energetic waves and can travel longer distances
without any loss of intensity.
2. They are reflected, refracted, scattered and absorbed like light waves.
3. They set-up standing waves in liquids and produce an acoustical
grating.
4. It can be propagated in different modes through the same material.
5. Ultrasonic can be propagated with different speed in different
medium.
(egs:-Velocity in air is 350 m/s& in water 1500 m/s.)
6. Based on the vibration of particles in the medium with respect to the
direction of propagation of ultrasonic’s. It can have four modes of
vibration
i) Longitudinal waves
ii) Transverse wave
iii) Surface wave
iv) Plate wave
7. Ultrasonic’s are highly energetic wave hence it can produce heat
effect in the medium.
8. Ultrasonic’s can accelerate some chemical reactions.
9. The different material can offer different acoustic impedance to the
flaw of ultrasonic’s.

Production of ultrasonic
1. Magnetostriction Method
In 1847 Joule discovered that, when a ferromagnetic materials
(Iron, Nickel etc) in the form of a bar is subjected to an alternating
magnetic field, Then the opposite pair of faces of the bar undergoes
continuous expansion and contraction, at a frequency equal to the
frequency of applied magnetic field. This phenomenon is called
Magneto-striction Effect.
The vibration caused by Magnetostriction effect in some ferro-
magnetic materials produces ultrasonic waves and is called
Magnetostriction method.

Working

The ferro-magnetic rod is inserted through the coils L 1 and L 2 as

shown in the figure. When the road is magnetized and demagnetized
with the current passing through L 1 and L2, the dimension of the road
varies accordingly and this vibration produces ultrasonic’s.
If the frequency of the vibrating rod is equal to the frequency of
the applied current, resonance occurs and the amplitude of vibrations
become very high and produces Ultrasonic waves. The frequency of
ultrasonic waves produced by this method depends upon the length ‘l’,
density ‘ρ’ and Elastic constant ‘Y’ of the bar.
1 𝑌
There for, Frequency ʋ =
2𝑙 𝛒

By varying the length of the bar, Ultrasonic waves of any desired

frequency can be generated

Piezo-Electric Method
In 1880 P.Curie and J.Curie discovered that, when a suitably cut
rectangular quartz crystal is subjected to stress, pressure or mechanical
squeeze then its opposite pair of faces becomes charged and generating a
potential difference across it. This phenomenon is called Piezo-Electric
Effect.
 When an Alternating potential difference is applied between any
two pair of faces of a rectangular Piezo-Electric crystal, then expansion
and contraction takes place in the opposite pair of faces of the material.
This phenomenon is called Inverse Piezo-Electric Effect.
The inverse piezoelectric effect is used for producing ultrasonic’s.
Whereas, Piezo-Electric Effect is used for detecting and measuring
ultrasonics.

Working

When the H.T(High Tension) battery is switched on, the

oscillating circuit produces high frequency alternating voltages with a
frequency ʋ. Due to the transformer action, an oscillatory e.m.f. is
induced in the coil L 3. This high frequency voltage is fed on to the plates
which placed across the quartz crystal and Inverse Piezo-electric effect
takes place. The crystal produces continuous contraction and expansion,
with the frequency equal to the frequency of applied AC voltage.
1 𝐸
The frequency of the vibration is given by, ʋ = 2𝑙 𝛒
Where,
E = Applied Electric field
𝛒= Density of the crystal.

The vibrating crystal produces longitudinal ultrasonic waves of

large amplitude, when an alternating potential difference is applied
between two opposite faces of a Piezo-Electric. The Crystal oscillates in
a direction perpendicular to the applied potential difference and
ultrasonic waves are produced. To avoid sparking at the quartz plate, a
spark gap is put parallel to it.
Detection of ultrasonics

1. Thermal Method
In this method a fine Platinum wire carrying current is moved
through the medium of ultrasonics. The temperature changes at nodes
and the temperature remains same at antinodes. The resistance is
proportional to the temperature, hence the resistance changes at the
nodes and remain constant at antinodes. This creates measurable
variations in the output voltage connected at the end of the platinum
wire. From these variations we can detect the presence of ultrasonic
waves in a medium.

2. Sensitive Flame Method

Ultrasonics will change the intensity of the flame. If we move a
candle flame, through the region where ultrasonics are spread. The flame
at the nodal plane becomes stiff and blue and at anti nodal region
becomes broaden and yellow.

3 Piezo-Electric Detectors
When a pair of faces of a piezoelectric crystal like quartz is
subjected to Ultrasonic waves, charges are developed across the opposite
pair of faces perpendicular to the first. These charges are amplified by an
amplifier and then detected by a suitable detector.

Non Destructive Testing (NDT)

The method of inspecting the internal structure of an object
without any disruption or impairment of their serviceability is called
NDT.

Uses of Ultrasonics
Ultrasounds are high frequency sound waves. They are able to
travel along well defined paths. Its different uses are:

1) To clean parts located in hard to reach places

Ultrasonic waves sent into the cleaning solution where the
objects to be cleaned are placed. The particles of dust, dirt and grease
get detached and drop out due to the high frequency. This help to
 clean the objects thoroughly. Spiral tube, electronic components and
odd shaped parts are examples of such hard to reach objects.
2) To detect cracks and flaws in metal blocks
Ultrasounds can be used to ensure safety and quality of metal used
in manufacturing of machines, scientific equipments, bridges and
buildings, etc.
When ultrasonic waves passed through the materials, the waves
redistributed according to the presence of flaws, cracks and other
structural deformities hidden inside the body. Detectors are also used
to detect the strength/quality of the metal blocks.
3) Echocardiography
It is the method in which ultrasonic waves are made to reflect from
various parts of the heart and form image of the heart.
4) Ultrasound scanner
This method is for obtaining the images of internal organs of
human body such as kidney, gall bladder, uterus, liver, etc. These
images of internal organs help the doctor to detect the abnormalities
such as tumors in different organs, stones in kidney and gall bladder,
etc.
In this technique, ultrasonic waves travels through the tissues of
the body and get reflected from a region where there is a change of
tissue density. This technique is also called ultra-sonography. Images
of internal organs are printed in the film or projected on a computer
monitor. During the pregnancy, to detect growth abnormalities of a
child at mother’s womb, doctors usually prescribe ultra-sonography
to examine the fetus.
5) To Break up Kidney stones
Another use of ultrasound is to break small stones formed in the kidneys
into fine grains. These grains later get flushed out with urine.
6) Sound Navigation and Ranging (SONAR)
It is a device that uses ultrasonic waves to measure the speed,
direction and distance of an underwater object. Sonar consists of a
detector and transmitter which are installed in a ship or a boat.
Transmitter emits ultrasonic waves and these waves travel through
the water. These ultrasonic waves get reflected back after striking the
object on the sea depth. The detector detects these waves and converts
into electrical signals which are appropriately interpreted.
 The sonar technique is used to determine the depth of
the sea and to locate icebergs, sunken ships, underwater hills, valleys,
submarine etc. By noting the time of travel, the depth of the sea or
position of submerged object can be found from the relation:
𝑣𝑡
d= 2
Where, v is the velocity of sound and d is the depth of the sea.
7) Ultrasonic welding
Utrasonic waves are used to weld thin metal sheets and foils.
The two pieces of metals are held in good contact by applying force.
Then highly intensed ultrasonic waves are passed through them and a
strong bond is created between the metals. This technique is
commonly used to weld plastics, aluminium, synthetic fabrics, films
etc. It is very useful in cell phones, disposable medical tools, toys etc.
8) Utrasonic mixing
When intensed ultrasonic waves are passed through
immiscible liquids, such as water and mercury or water and oil, they
are transformed into highly stable emulsions.
9) Elastic Symmetry of Crystals
The phenomenon of acoustic grating is used to study the
elastic symmetry of crystals. If an ultrasound wave is passed through
a solid or liquid and a beam of light is allowed to travel in a direction
perpendicular to it. Then the ultrasonic wave system will act as an
acoustic grating. The compressions will act like opacities and
rarefactions as transparencies. Ultrasonics are allowed to pass on an
isotropic crystal, we get interference fringes from which the elastic
symmetry of the crystal may be studied.
10) Biological Effects
Small animals like fish, frog etc., can be killed when exposed
to ultrasonics. Ultrasonics are very useful in medical sciences.These
waves have been found to be very useful for neuro patients where
other conventional methods like electric shock, physiotherapy, etc.
Ultrasonics are also used to locate eye tumor.

11) Acoustic Diffraction Method

When an ultrasonic wave propagates in liquid medium, the
alternating compression and rarefactions changes the density of the
medium. It leads to a periodic vibration of refractive index of the liquid.
Thus, the liquid column which is subjected to ultrasonic wave acts as
grating called acoustic grating.
When a monochromatic light of wavelength ‘λ’ passed
through the liquid column, produces a diffraction pattern. By comparing
it with grating equation we can determine wavelength and velocity of
ultrasonics.

We have grating equation, d sinθ= nλ

𝛌𝐮
Here , d= , grating element
2
𝛌 𝐮 – Wavelength of Ultrasonics.
𝛌𝐮
Hence grating equation become, sinθ= nλ
2

𝟐𝐧𝛌
Wavelength of Ultrasonics, 𝛌 𝐮 = 𝐬𝐢𝐧𝛉

𝟐𝐧𝛌 𝐮 𝛄𝐮
Velocity of ultrasonics, 𝒗 𝒖 = 𝐬𝐢𝐧𝛉

θ – angle of diffraction
uγ − Frequency of ultrasonics