3.1.

1 Echo
3.1.2 Reverberation
3.1.6 Absorption of sound and Absorption
Co-efficient
3.2.1 Sabine’s Law
3.2.2 Acoustics of Building
3.2.3 Sound Distribution in an Auditorium
3.2.4 Requisites for good Acoustics
3.3.1 Ultrasonic Waves
3.3.2 Production of Ultrasonic Waves
3.3.3 Application of Ultrasonic Waves
3.1.1 Echo
When a sound is produced in front of a distant big
obstacle such as cliffs, walls, etc., it will be reflected back
and under suitable condition, the sound can be heard
again and again, i.e. the sound is repeated. This
repetition of sound from a distant object is called echo. If
an observer produces sound and it is reflected back to
the observer in time, t from an obstacle (cliff or wall)
which lies at a distance, x from the observer, then the
minimum distance that is covered by the sound must be
2𝑥
equal to 2x so that 𝑡 = , where v is the velocity of
𝑣
𝑣𝑡
sound. So, 𝑥 = .
2

2
Contd….
Since the velocity of sound in air at N.T.P.is 332 m/s and
the persistence of hearing for normal human ear is 1/10
sec, i.e. the effect of sound on human ear remains for
1/10 of a second, the minimum distance between the
observer and reflector to observe the sound clearly and
1
332𝑥 10
distinctly is given by 𝑥 = ≈ 17 𝑚. Hence, for an
2
echo to be heard clearly, the minimum distance between
the observer and reflector should be 17m. If the distance
between the reflector and observer is less than 17m, the
echo cannot be heard clearly. The knowledge of echo is
used in sonar in order to determine the location of distant
objects like underwater rocks, icebergs, whales, etc.
Similarly, it is also used in radar.
3
3.1.2 Reverberation
When a sound is produced by a source in a room or an
auditorium, an observer receives sound waves from the
source directly as well as reflected sound waves from
the walls, ceiling and other materials present in the
room. The sound waves received by the listener are :
a) direct waves and b) reflected waves due to multiple
reflections on the surfaces of various objects. The
quality of the note received by the observer will be the
combined effect of these two sets of waves. The
reflected sound waves reach to the observer with a
time delay. This delay between the direct and reflected
sounds results in the distortion and disorientation of the
quality of sound.

4
Contd…..
If the distance between observer and reflector is less
than 17m, the time interval between the direct wave
and reflected wave to reach the observer is less than
1/10 sec which cannot be detected clearly by the
normal human ear due to persistence of hearing. Due
to this, the sound persists in the room for some time
even after the sound has stopped. This phenomenon
of lingering of sound after the source has been cut off
in the room, is called reverberation. The time gap
between the direct sound and reflected sound up to
the minimum audibility level in the room is called
reverberation time. It depends upon the size of the
room, the area of the reflecting surfaces and the
nature of reflecting material on the wall, ceiling, etc..
5
Contd…..
When a sounding body
produces sound A

Sound Density
energy continuously,
the sound energy per Reverberation Time
unit volume (i.e. sound
density) at the
beginning is small but O C B Time
it goes on increasing Fig-3.1: Graph for sound Intensity versus Time
due to multiple
reflection of sound
from walls, ceilings,
floors, etc. till a
maximum steady value
is reached as
represented by the
curve OA in the figure-
3.1 6
Contd…..
If the source of sound is cut off, the sound density does
not fall to zero suddenly but takes time to decay as
represented by the curve AB in the figure. Thus, the
sound persists in the room before becoming inaudible for
a while after the cut-off of sound source. The time for
which the sound persists in the room after cutting the
sound source is called reverberation time which is
represented by BC in the figure. The desirable value of
reverberation time for music is 1 sec to 2 sec but for
speech is 0.5 sec to 1 sec. For clear audibility of speech
or music inside a room, it is necessary that:
I. Each separate note gives sufficient intensity of sound
in every part of the room.
II. Each note should die down rapidly before the
maximum average intensity due to next note heard by
the listener. 7
3.1.3 Acoustics of Building
The branch of physics which deals about the process
of generation, reception and propagation of sound is
called acoustics. This branch, In fact, covers various
fields, closely related with the many branches of
engineering. Some of them are:
I. Acoustical instruments designing
II. Electro-acoustics (the branch relating to the
methods of sound production and recording such
as loudspeakers, microphones, etc.)
III.Architectural acoustics (dealing with the design and
construction of buildings, halls, recording rooms of
radio/TV broadcasting stations)
IV.Musical acoustics (dealing with the design of
musical instruments)
8
Contd….
There are so many factors affecting the acoustics of
buildings which are as follows:
Reverberation Time: It is one of the most important factor
affecting the acoustics of a room/hall. It should have
optimum value, i.e. should not be too large or too small.
Also, there should be no echo.
Loudness: To ensure uniform distribution of sound intensity
in in every part of a hall, electrically amplified loud
speakers are kept in different places at a height higher
than the observer’s head.
Focusing: The presence of cylindrical or spherical surfaces
on the walls or the ceiling gives rise to undesirable
focusing of sound at a point so that the sound intensity
may be maximum or minimum at that point in comparison
to the other part. Thus, the wall and ceiling of the hall
should be designed such that the sound intensity is
uniform at any point inside the hall.
9
Contd….
Extraneous Noise: The extraneous noise may be due to: I)
sound received from outside the room, II) the sound produced
inside the room such as by fan, A.C., etc. Such extraneous noise
cannot be removed completely but can be minimized by taking
suitable precautions.
Resonance: If there is resonance for a sound wave of a
particular frequency, the intensity of that sound is extremely high
in comparison to desired intensity. In hall of large size, the
resonance frequency is much smaller than the audible limit so
that harmful effects due to resonance will be omitted.
Echelon effect: If there is regular structure such as a set of
railings in a hall, the sound produced in front of such a structure
may produce a musical sound due to regular successive echo of
sound reaching to the observer. Such an effect is called echelon
effect. If the frequency of such a sound lies within the audible
range, the observer may receive this sound prominently. To
avoid echelon effect, the railings may be covered with carpet to
avoid the reflection on sound.
10
3.1.4 Sound Distribution in an Auditorium
A good auditorium requires smooth decay and growth
of sound in such a way that the sound must be
distributed and diffused uniformly over the whole area.
These factors can be achieved by using various good
acoustic treatments such as scattering effect of
objects, irregularities on the wall surfaces, fixing
absorptive material on the walls, designing the proper
construction of walls and ceiling, etc. The uniform and
equal distribution of sound inside an auditorium can be
achieved by constructing the auditorium properly as
shown in figure-3.2.
The first reflection of sound waves at different positions
of ceiling is shown in the above figure so that reflected
sound is distributed uniformly in the auditorium which
gives uniform distribution of sound intensity. 11
Contd……

Fig-3.2: Uniform sound distribution in

12
3.1.5 Requisites for good Acoustics
In a good auditorium, the reverberation time should be
reduced below the optimum value which can be
obtained by using the surfaces with high absorption
coefficient. So the acoustics of an auditorium can be
improved by taking following ways:
1. By hanging heavy curtains (a screen of heavy
material that can be raised or lowered at the front of
stage)
2. By having a few open windows
3. By hanging pictures or maps
4. By avoiding the curved walls and corners bounded
by two walls to remove the unnecessary
concentration or lacking of sound at different
locations in auditorium 13
Contd…..
5. By having good audience, because each person is
equivalent to 0.5 sq. metre area of an open window
6. By covering the walls and ceilings with materials having
high absorption coefficient
7. By covering seats and other materials by soft materials so
as to produce approximately same absorption with or
without audience
During the design of auditorium, it should be in mind that the
reverberation time should not be decrease much below the
optimum limit which depends upon the design of the
auditorium and the purpose for which it is used. If the
reverberation time is small, most of the sound energy is
absorbed and the average sound intensity in the auditorium
may fall below audible limit so that auditorium appears dead.
14
3.1.6 Absorption of sound and
Absorption Co-efficient
The reverberation time in an auditorium or hall can be
adjusted by varying the absorption of sound which depends
upon the nature of the materials and their surface area
present in the hall. The absorption coefficient of sound of a
surface is the ratio of sound energy absorbed by the
surface to the sound energy absorbed by an equal area of
a perfect absorber. An open window is an example of a
perfect absorber because of total transmission of sound but
not reflection. If 𝛼1 , 𝛼2 , 𝛼3 , … ., be the absorption coefficients
of the respective absorbing surface of area 𝑆1 , 𝑆2 , 𝑆3 … … , ,
made by different materials forming the interior surface of
the room, the total absorption is given by 𝐴 = 𝛼𝑖 𝑆𝑖 .
Thus, the average absorption coefficient is given by 𝛼 =
𝛼𝑖 𝑆𝑖
------ (3.1)
𝑠𝑖
15
3.2 Sabine’s Law
Sabine derived an empirical relation between the
reverberation time, the volume and dimensions of a
hall to represent the rise and fall of sound in the hall.
Let us assume a source of sound which produces
sound continuously and propagates in all direction. If
σ is the energy contained in a unit volume, the
𝜎 (𝑑𝜙)
energy contained in a solid angle 𝑑𝜙 will be . If v
4𝜋
be the velocity of sound energy which is incident on a
unit surface area of the wall at an angle 𝜃, then the
total energy falling per second on a unit surface area
𝜎 (𝑑𝜙)
of the wall will be 𝑣 cos 𝜃 . Thus, the total
4𝜋
energy falling per second within a hemisphere is
given by 16
Contd…
𝜋 𝜃
𝜎𝑣
𝐸= 0
2 cos 𝜃 𝑑𝜙 ------ (3.2) 𝜙
4𝜋
But, 𝜙 = 2𝜋(1 − cos 𝜃) Fig-3.3: Solid Angle
i.e. 𝑑𝜙 = 2𝜋 sin 𝜃 𝑑𝜃
𝜋
𝜎𝑣 𝜎𝑣
Thus, 𝐸 = 0
2 2 𝜋 sin 𝜃 cos 𝜃 𝑑𝜃 = ----- (3.3)
4𝜋 4
If the absorption coefficient of the wall is 𝛼, then the
amount of energy absorbed per unit time per unit area
𝛼𝜎 𝑣
will be .
Thus, the amount of energy absorbed in
4
unit time by the walls and other absorbing materials of
𝐴 𝛼𝜎 𝑣
area, A is given by 𝐸𝑇 = ----- (3.4)
4

17
Contd…
If V be the volume of auditorium, the total energy will
be 𝑉𝜎 so that increase in energy per unit time is
𝑑 𝑑𝜎
given by 𝑃 = 𝑉𝜎 = 𝑉 ----- (3.5)
𝑑𝑡 𝑑𝑡
Suppose the source supplies energy at the rate of Q
units per second so that the rate of increase of
𝐴 𝛼𝜎 𝑣
energy is given by 𝑃 = 𝑄 − 𝐸𝑇 = 𝑄 − ----- (3.6)
4
On comparing equations (3.5) and (3.6), we have
𝑑𝜎 𝐴 𝛼𝜎 𝑣
𝑉 =𝑄−
𝑑𝑡 4
𝑑𝜎 𝑄 𝐴𝛼𝑣
i.e. = − 𝜎 ----- (3.7)
𝑑𝑡 𝑉 4𝑉

18
Contd…
𝐴𝛼𝑣 𝑋 𝑄 4𝑄
Let = 𝑋, = 𝛽 𝑎𝑛𝑑 𝑌 = = ----- (3.8)
4 𝑉 𝑋 𝐴𝛼𝑣
Then by equation (3.7), we have
𝑑𝜎 𝑄 𝑋
= − 𝜎 ----- (3.9)
𝑑𝑡 𝑉 𝑉
The general solution of equation (3.9) will be
𝑋
4𝑄 − 𝑡
𝜎 = 𝑌 1 − 𝑒 −𝛽𝑡 = 1−𝑒 𝑉
𝐴𝛼𝑣
𝐴𝛼𝑣
4𝑄 − 𝑡
= 1−𝑒 4𝑉 ----- (3.10)
𝐴𝛼𝑣

19
Contd…
So, the maximum value of average energy per unit
4𝑄
volume will be 𝜎𝑚𝑎𝑥 = and the decay of the
𝐴𝛼𝑣
average energy per unit volume after the source ceases
to emit sound is given by
𝐴𝛼𝑣
4𝑄
𝜎0 = 𝑒− 4 𝑉 𝑡 ----- (3.11)
𝐴𝛼𝑣
𝐴𝛼𝑣
i.e. 𝜎0 = 𝜎𝑚𝑎𝑥 𝑒− 4 𝑉 𝑡 ----- (3.12)
𝜎0
𝜎𝑚𝑎𝑥

𝜎max 𝑥10−6
t
𝜏
20
Contd…
If 𝑡 = 𝜏 (reverberation time), 𝜎0 decreases to minimum
audible sound energy for normal human ear, which is
equal to 𝜎𝑚𝑎𝑥 𝑥10−6 . So, by using equation (3.12), we
have
𝐴𝛼𝑣
𝜎𝑚𝑎𝑥 𝑥10−6 = 𝜎𝑚𝑎𝑥 𝑒− 4 𝑉 𝜏
𝐴𝛼𝑣
i.e. 𝜏 = ln 106
4𝑉
0.165 𝑉
i.e. 𝜏= (if we take 𝑣 = 332 𝑚/𝑠) ----- (3.13)
𝐴𝛼
Which represents Sabine’s Law

21
3.3.1 Ultrasonic Waves
Normal human ear can detect the sensation of hearing
of sound waves of frequency ranging from 20 Hz to 20
KHz, which is called audible range. Sound waves of
frequency lower than the audible limit are called
infrasonic, while the sound waves of frequency higher
than the audible limit are called ultrasonic. Ultrasonic
waves have a large number of practical applications.
3.3.2 Production of Ultrasonic Waves
It is very difficult to produce waves carrying high
frequency, i.e. Ultrasonic waves with the help of
mechanically oscillating object only. So, they can be
produced by oscillating object using its mechanical,
electrical and magnetic properties as discussed below:
22
Contd….
1) Magnetostriction method
If a rod, made by ferromagnetic substance is kept
inside a solenoid carrying high frequency a.c., the
length of the rod will change periodically which will
generate longitudinal waves in surrounding. If the
frequency of a.c. is more than 20 kHz, the waves thus
produced carries the frequency more than 20 kHz
which are known as Ultrasonic waves.
2) Electrostriction method (Piezo-electric method)
The phenomenon of developing opposite electric
charges in a pair of opposite faces of an asymmetric
crystal on applying pressure to the other pair of
opposite faces of the crystal is called Piezo-electric
effect.
23
Contd….
When the opposite faces are subjected to tension in turn
of pressure, the sign of charges change. Further, the
converse of Piezo-electric effect is also observed. So, if an
alternating voltage is applied to one pair of opposite faces
of such a crystal, the dimensions of other pair of faces of
the crystal change which can further be increased by using
thin slices of crystals of quartz, tourmaline, etc. Thus,
when the two opposite faces of a quartz crystal, cutting its
faces perpendicular to the optic axis (optic axis- the
direction in a doubly refracting crystal in which light is
transmitted without double refraction) are subjected to
alternating voltage, other pair of opposite faces experience
stress and strains so that the quartz crystal continuously
contracts and expands and hence, elastic vibrations are
set up in the crystal.
24
Contd….
When the frequency of the applied alternating voltage
is equal to the natural frequency of vibration of the
crystal, or its integral multiple, the crystal is set to
resonant vibrations and the amplitude will be large.
These vibrations are longitudinal in nature and the
frequency of vibration is represented by
𝑃 𝑌
𝑓=
2𝑙 𝜌

Where 𝑝 = 1, 2, 3, … … .
Y = Young’s modulus of elasticity of the crystal
𝜌 = Density of the crystal
l = length of the crystal
25
Contd….
Since the velocity of longitudinal waves in quartz
𝑌
crystal is 𝑣 = = 5.5𝑥103 m/s, the frequency for the
𝜌
1
1st mode of vibration will be 𝑓 = 𝑥5.5𝑥103
=
2𝑥0.05
5.5𝑥104 𝐻𝑧 , if the length of the crystal is equal to
0.05m. So, other modes of frequency are equal to
integral multiple of 5.5𝑥104 𝐻𝑧 , which represents
Ultrasonic waves

26
3.3.3 Application of Ultrasonic Waves
Ultrasonic waves have a number of practical
applications which are as follows:
1. Distance measurement (eg: Depth of Sea): To
measure the depth of sea, ultrasonic waves of
high frequency are directed towards the bed of the
sea and reflected waves are detected. By
measuring the time interval between the
transmission and receipt of the ultrasonic waves,
𝑣𝑡
the depth of sea, i.e. ℎ = , can easily be
2
calculated where v is the velocity of the ultrasonic
waves and t is time taken by ultrasonic wave to
return back after reaching bed of the sea.
2. Medical application: Ultrasonic waves have a
number of application in the field of medical
science. 27
Contd…..
a. Diagnostic work: The ultrasonic waves are
transmitted through a patient and then
reflected or refracted waves are analyzed to
locate the growth of organs such as tumors.
b. Neuralgic and rheumatic pain: The affected
portion of the body is exposed to ultrasonic
waves which produce a soothing massage
action and relieves pain.
c. Bloodless surgery: Ultrasonic waves of very
high frequency is focused on the affected
tissues which are then destroyed without any
loss of blood.
d. Broken teeth: Ultrasonic waves are used by
dentists for proper extraction of broken teeth.
28
Contd…..
3) Detection of cracks in metals: Ultrasonic
waves are directed towards the metal and
reflected beam is detected by detector. By
analyzing the energy received by the detector,
we can easily detect the cracks or discontinuity
in metal structures.
4) Signalling: Ultrasonic waves are used for
directional signalling. Since the frequency of
ultrasonic waves is higher than the audible
sound waves, the wavelength of ultrasonic
waves is comparatively small, hence they can
be sent in the form of short beam. Thus, large
amount of energy is radiated.
29
 Contd…..
5) Sterilization: Ultrasonic waves can destroy unicellular
organisms so that they are used in sterilization of water and
milk.
6) Enemy of lower life: When ultrasonic waves are exposed to
lower animals like rats, frogs, fishes, etc. they become lame
(unable to walk).
7) Soldering: Ultrasonic waves remove the oxide film and
facilitates soldering so that they are used in addition to
electric soldering iron to solder aluminum.
8) Heating effects: When a beam of ultrasonic waves passes
through a substance, it gets heated so that ultrasonic waves
are also used for heating purpose.
9) Chemical effects: Ultrasonic waves act as catalytic agents
and accelerate chemical reactions so that they bring a
number of chemical changes.
10)Mechanical effects: Ultrasonic drills are used to bore holes
in steel and other hard metals or their alloys.
30