Unit - II : Architectural

Acoustics

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 Intensity of Sound

• The sound waves transport energy from source to listener and the amount of
energy that flows per second across the unit area in the direction of propagation is
called the intensity of the wave.

𝐸𝑛𝑒𝑟𝑔𝑦
𝐼𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 =
𝐴𝑟𝑒𝑎 × 𝑇𝑖𝑚𝑒

𝑃𝑜𝑤𝑒𝑟
𝐼𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 =
𝐴𝑟𝑒𝑎

• The unit used for intensity is W/m2 or W/cm2.

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 Loudness
• Loudness is the characteristic of all sound. It is associated with the
intensity of sound which is a definite physical quantity. But there is
a marked difference between the loudness and the intensity of
sound.
• Loudness of a sound is the degree of sensation depending on the
intensity of the sound and the sensitiveness of the ear. Loudness
does not increase proportionally with intensity but as its logarithm.
• According to Weber and Frechner's law,
L α log I ... (1)
• where L represents the sensation of loudness and I the intensity of
sound. Since loudness is the degree of sensation and depends on the
ear of the listener, it cannot be measured by physical apparatus.
• However, the greater the intensity of sound, the greater its loudness.
The loudness of sound depends on all the factors on which the
intensity of sound depends.

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 Intensity and Intensity level
• The loudness of a sound 'L' as judged by the law is proportional to the
logarithm of the intensity.
L α log I
• If I1 and I0 represent the intensities of two sounds of a particular
frequency, and L1 and L0 the corresponding measures of loudness, then,
L1 α log10 I1
L1 = K log10 I1
Similarly L0 = K log10 I0
• The difference in loudness is the Sound intensity level (SIL) or Sound pressure
level (SPL).
• The unit of SPL is Bel but the unit decibels is more frequently used. 1 decibel
(dB) is 1/10 th of a Bel.

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 Pressure and Intensity level
S.I.L. = L1 – L0 = K [log10 I1 – log10 I0]
S.I.L. = K log10 I1/I0... (1) where K is a constant that depends on the units.
• I0 is the standard reference intensity taken as 10–16 watts/cm2 or 10–12 watts/m2,
corresponds to the intensity of sound, which can be just heard at a frequency of
about 1000 hertz. This is taken as the threshold of audibility of a normal ear.
S.I.L. = log10 I1/I0 B or
S.I.L. = 10 log10 I1/I0 dB
• The intensity is related to the pressure by the following relation

……..(2) 𝒑𝟐
𝑰=
𝟐𝝆𝟎 𝒗
• P - effective pressure of the sound wave, ρ0 - is the density of medium, v -
velocity of sound
• The intensity is proportional to the square of pressure, the sound pressure level
(SPL) or intensity level (I.L.) is given by
𝑷
𝑺𝑷𝑳 = 𝟐𝟎 𝐥𝐨𝐠 𝟏𝟎
𝑷𝟎
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Where, Po is the reference standard pressure = 2 * 10–5 Newton/m2
 REVERBERATION/ REVERBERATION TIME
• Reverberation – Whenever sound is produced in a hall, it lasts for quite
sometime. This is because sound waves keep on reaching the listener a number of
times. “ The persistence or prolongation of sound in the hall even after the sound
source has been stopped is called reverberation ”
• Reverberation Time – “The time during which sound persists in the hall is called
reverberation time.” or “The time taken by sound to fall from its average intensity
to inaudibility” or “The time taken by sound to fall from its steady state value to
one millionth value”

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 Factors on which reverberation time depends

1. The reverberation depends on the reflecting properties of the

walls, floor, and ceiling. If they are good reflectors, then
sound would take a long time to die away. Hence, the
reverberation time would be large.

2. The reverberation depends on the coefficient of absorption of

various surfaces such as carpets, cushions, curtains, and
furniture present in the room. The greater the absorption, the
lesser the time of reverberation.

3. The reverberation time depends on the frequency of the note.

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 Importance of Reverberation Time
1. If a building is to be acoustically good, it is very important that its
reverberation time must be optimum. It should not be too short
or too long. A very short reverberation time makes a room sound
dead. The sensation of speaking in such a room is similar to that
experienced when speaking from the top of an isolated building.
2. A long reverberation time is more undesirable than a short one. It
confuses and renders speech unintelligible and music dissonant.
3. The best value for reverberation time depends on the use for which
a building is designed.
4. A certain amount of reverberation is desirable. Because this adds
pleasing characteristics to the acoustical qualities of a room. Too
much reverberation is undesirable, while too small reverberation
has a deadening effect on the sound. Hence, obtaining the right
amount of reverberation is the secret of good acoustics.

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 SOUND ABSORPTION
• When a sound wave strikes a surface, the total sound energy is distributed in three
ways. A part of its energy is transmitted across the surface, a part of its energy is
absorbed by friction, and the remaining of its energy is reflected by the surface. The
property of a material that converts sound energy into other forms of energy is known
as absorption.
• The sound generated in an auditorium or hall is absorbed in four ways
(i) Absorption by Air: The absorption of sound in air is mainly due to the friction
between the oscillating molecules when a sound wave travels through it.
(ii) Absorption by Audience: Sound energy is absorbed by the clothing of the audience.
Room acoustics change appreciably by the number of audience present. Absorption is
more in winter than in summer due to heavy clothing.
(iii) Absorption by Furniture and Furnishings: Furniture, curtains, carpets, etc.
also absorb sound energy.
(iv) Absorption by Boundary Surface: When sound waves strike the boundary
surface such as walls, floors, and ceilings absorption takes place due to the following
factors :
(a) Penetration of sound into porous materials. This causes resonance within air
pockets in the pores until energy is dissipated. (b) Resonant vibration of panel
materials. (c) Molecular damping in soft absorbing materials. (d) Transmission
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through structures.
 SOUND ABSORPTION COEFFICIENT
• When sound energy is incident on a surface, a part of the energy is absorbed by
the surface. Different surfaces have different sound absorption capacities. This
capacity depends upon the nature of the surface.
• The coefficient of absorption of a surface is defined as the ratio of the sound
energy absorbed by it to that of the total sound energy incident on the
surface.
• i.e. Absorption coefficient 'a’ = Sound Energy absorbed by the
surface/Total Sound Energy incident on the surface

• An open window allows all sound energy incident on it to pass through and it
reflects none of the sound energy incident on it. Hence an open window is
considered as a perfect sound absorber and an open window of unit area is
chosen as the standard for expressing absorption of sound.

• Total absorption by material = Absorption coefficient X Area of material.

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 Sabine’s formula
Prof. W. C. Sabine of Harward University studied the reverberation time of an empty
and furnished hall. The conclusions are as follows
• The reverberation time depends upon reflecting properties of surfaces
• The reverberation time depends upon the volume V of the hall – directly
• The reverberation time depends upon the absorption ‘a’ of the hall – inversely
• The reverberation time depends upon the frequency of sound

T α V/A or T= k V/A

A - Total absorption of the hall, V - is the volume of the room, K - is the

proportionality constant.
For auditorium having large number of absorbing materials having different surface
area, the total absorption will be the sum of absorptions due to individual absorbing
material.
𝑽
𝑻=𝒌
∑𝒂𝒏 𝑺𝒏
A = Σa.s = a1 .s1 + a2 s2 + ..... + an sn
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 Sabine’s formula
If V is in cubic meters and S is in square meters, K = 0.165
If V is in cubic feet and S is in square feet, K = 0.05

𝑉
𝑇 = 0.165 in M.K.S. system
𝐴

𝑉
𝑇 = 0.05 in British system
𝐴

This equation is called Sabine's formula for reverberation time.

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 DIFFERENT TYPES OF NOISE AND THEIR REMEDIES

• Noise can be defined as unwanted sound.

Air-Borne Noise: The noise that reaches the hall from outside through air is called
air-borne noise. In this, the noise is transported by air through the open vent, window,
door, etc. The air-borne noise can be reduced by

• avoiding ventilators facing the streets,

• placing doors and windows at the proper place,

• using heavy glass doors, windows, and ventilators,

• having double wall construction.

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Structure-Borne Noise: The noise that is conveyed through the structure of a
building is known as structural noise. This noise is caused by structural vibrations
due to construction activities like hammering, drilling, operating machinery, etc. The
structure-borne noise can be reduced by

• breaking the continuity of the structure,

• using double wall,

• using anti-vibration mounts like rubber pads.

Inside Noise: The noise that is produced inside the hall is called inside noise. They
are produced by equipment and machinery used in the hall. This can be reduced by

• placing machinery on insulating pods,

• covering floor with carpets,

• sound absorbing materials should be placed close to noise producing source.

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 Factors affecting the architectural acoustics & their remedies

(1) Reverberation: In a hall, when the reverberation is large, there is an

overlapping of sound. This will lead to a lack of clarity in hearing. If the
reverberation is small, there is a deadening effect on sound. As a result, the
loudness becomes inadequate.

(2) Reverberation should have an optimum value. This value can be calculated by a
formula given by Prof. W. C. Sabine. Reverberation time can be controlled in the
following ways

– By providing sound-absorbing materials on the walls and using carpets on the

floor.

– Using curtains and providing acoustic tiles.

– Providing windows and ventilators.

– Having furniture and audience. PPW 15

 Factors affecting the architectural acoustics & their remedies

(2) Echoes: An echo is heard when reflected waves from the same source
reach the listener with a time delay of 1/10th of a second. The reflected sound
arriving earlier than this helps in raising the loudness while that arriving later
produces echoes and causes confusion.
• Echoes can be reduced or avoided by covering long distant walls and high
ceilings
• Use of absorbent materials like felt, perforated cardboard, coarse cloth, etc.

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 Factors affecting the architectural acoustics & their remedies

(3) Loudness: The control of reverberation may lead to the reduction in the
intensity of sound. Hence the level of intelligible hearing goes down. For
satisfactory hearing, sufficient loudness in every part of the hall is very
important. The loudness can be increased by
• providing loudspeakers,
• providing sounding boards behind the speaker and facing toward the
audience,
• Providing wooden reflectors above the speaker

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 Factors affecting the architectural acoustics & their remedies

(4) Focusing due to Walls and Ceiling (sound focii): Focusing surfaces like
curved surfaces on the walls or ceiling produce concentration of sound in particular
regions, while in some other parts, no sound is heard at all. This leads to poor and
uneven sound intensity distribution. Uniform sound distribution can be achieved by

• avoiding and or covering curved surfaces with sound-absorbent materials,

• having a low ceiling,

• providing parabolic reflectors behind the speaker with the speaker at the focus.

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 Factors affecting the architectural acoustics & their remedies

(5) Echelon Effect: Regular succession of echoes occur when sound is reflected
from equally spaced reflecting surfaces like a staircase or a set of railings. This
effect is known as Echelon effect. This makes the original sound confusing or
unintelligible. This effect can be reduced by

• Covering the stairs with thick carpets

• Breaking the regularity of spacing of the steps.

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 Factors affecting the architectural acoustics & their remedies

(6) Resonance: Sometimes window panes and other parts of the structures that
are not rigid are thrown into vibrations and they create other sounds.
• If some note of the audio frequency and the frequencies of new sounds are
the same, then resonance occurs.
• Due to the interference between the original sound and the created sound, the
original sound is distorted.
• Thus the intensity of the note is entirely different from the original one. Also,
enclosed air in the hall causes resonance.
• Such resonant vibrations should be suitably damped.

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 Factors affecting the architectural acoustics
(7) Seating Arrangement: The speaker or source of sound should be at the focus of
a parabolic reflecting surface. The seats should be arranged such that they are
perpendicular to the direction of sound. The seats should be gradually elevated. This
arrangement ensures uniform distribution of sound.

8) Balconies: The balconies should have shallow depths and high openings. They
should have railing bars instead of walls. This allows sound energy to flow readily
into the space of the balcony.

(9) Noise: An external noise makes speech or music makes the sound unintelligible.
The noise may come to room by air or structure. The noise could be reduced by
sound insulation. The noise in the hall should be minimal so that the sound is heard
clearly. PPW 21
 Basic requirement for acoustically good hall
• In architectural acoustics, we deal with the behavior of sound in an auditorium. Many
times it is found that in an auditorium, sound cannot be heard clearly. Either intensity
at some places is not high enough or repeated speeches are heard. To make a hall
acoustically good, it should have the following features.

• The sound must be loud enough in every part of hall.

• There should not be repeated speeches heard in the hall. i.e. free of echo.

• There should not be overlapping of speeches, i.e. reverberation time should have
optimum value.

• Focusing of sound should not be there.

• Should be free of echelon effect.

• Should be free of resonance.

• External sound (noise) should be minimum.

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 Ultrasonics

• A vibrating body produces sound. Human audible range is 20 Hz to 20

KHz.
• Sound waves of frequency greater than 20 KHz are Ultrasonic waves.
So wavelength is very small. Frequencies used for medical diagnostic
ultrasound scans extend to 10 MHz and beyond.
• Below human audible range i.e. 20 Hz are infrasonic/subsonic waves.
Dogs, bats can hear ultrasonic sound.
• Ultrasonic waves can not be produced by normal mechanical vibration
method. A device which produces ultrasonic waves is ultrasonic
transducer.
• Magnetostriction generator (upto 30KHz) and Piezoelectric generator
are the methods used for production of Ultrasonic waves.

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 Properties of Ultrasound

 They have high energy, and high frequency.

 Just like ordinary sound waves, ultrasonic waves get reflected,
refracted and absorbed.
 They can be transmitted over large distances with no appreciable
loss of energy. Small wavelength – less diffraction
 If an arrangement is made to form stationary waves of ultrasonics
in a liquid, it serves as a diffraction grating. It is called an acoustic
grating.
 They produce intense heating effect when passed through a
substance.
 Velocity of ultrasonic waves depends upon temperature of
medium.
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 MAGNETO-STRICTION GENERATOR

Principle: When a ferromagnetic rod like iron or nickel is placed in a

magnetic field parallel to its length, the rod experiences a small change
in its length. This is called Magnetostriction effect.

The change in length (increase or decrease) produced in the rod

depends upon the strength of the magnetic field, the nature of the
materials and is independent of the direction of the magnetic field
applied.

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 MAGNETO-STRICTION GENERATOR - Construction
• AB is a rod of
ferromagnetic materials
like iron or nickel. The
rod is clamped in the
middle.

• The alternating magnetic

field is generated by
electronic oscillator.

• The coil L1 wound on the right hand portion of the rod along with a variable
capacitor C.
• This forms the resonant circuit of the collector tuned oscillator. The frequency of
oscillator is controlled by the variable capacitor.
• The coil L2 wound on the left hand portion of the rod is connected to the base
circuit. The coil L2 acts as feed –back PPW
loop. 26
 MAGNETO-STRICTION GENERATOR - Working
• When the High Tension (H.T) battery is switched on, the collector circuit
oscillates with a frequency 𝟏
𝒇=
𝟐𝝅 𝑳𝟏 𝑪
• This alternating current flowing through the coil L1 produces an alternating
magnetic field along the length of the rod. The result is that the rod starts
vibrating due to magnetostrictive effect.
• The frequency of vibration of the rod is given by
𝟏 𝒀
𝒇=
𝟐𝒍 𝝆

l = length of the rod, Y = Young’s modulus, ρ = density of rod material

• The capacitor C is adjusted so that the frequency of the oscillatory circuit is
equal to the natural frequency of the rod and thus resonance takes place.
• Now the rod vibrates longitudinally with maximum amplitude and generates
ultrasonic waves of high frequency from its ends.
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 MAGNETO-STRICTION GENERATOR - Working

Advantages –
• The design of this oscillator is very simple and its production cost
is low
• At low ultrasonic frequencies, the large power output can be
produced without the risk of damage of the oscillatory circuit.

Disadvantages –

• It has low upper frequency limit and cannot generate ultrasonic

frequency above 3000 kHz (ie. 3MHz).
• The frequency of oscillations depends on temperature.
• There will be losses of energy due to hysteresis and eddy current.

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 PIEZO ELECTRIC GENERATOR

• Principal – Piezoelectric effect.

If mechanical pressure is applied to one pair of opposite faces of
certain crystals like quartz, equal and opposite electrical charges
appear across its other faces. This effect is called as piezo-electric
effect.

• The converse of piezo-electric effect is also true. If an electric

field is applied to one pair of faces, the corresponding changes in
the dimensions of the other pair of faces of the crystal are
produced. This effect is known as inverse piezo electric effect.

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 PIEZO ELECTRIC GENERATOR - Construction

• The quartz crystal is placed between two metal plates A and B.

• The plates are connected to the primary (L3) of a transformer which is
inductively coupled to the electronics oscillator.
• The electronic oscillator circuit is a base tuned oscillator circuit.
• The coils L1 and L2 of oscillator circuit are taken from the secondary of a
transformer T.
• The collector coil L2 is inductively coupled to base coil L1.
• The coil L1 and variable capacitor C1 form the tank circuit of the oscillator.
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 PIEZO ELECTRIC GENERATOR - Construction
• When the H.T. battery is switched on, the oscillator produces high-frequency
alternating voltages with a frequency 𝟏
𝒇=
𝟐𝝅 𝑳𝟏 𝑪𝟏
• Due to the transformer action, an oscillatory e.m.f. is induced in the coil L3. These
high-frequency alternating voltages are fed on plates A and B.
• Inverse Piezo-electric effect takes place and the crystal contracts and expands
alternatively. The crystal is set into mechanical vibrations.
• The frequency of the vibration is given by 𝑷 𝒀
𝒇=
𝟐𝒕 𝝆

P= 1,2,3,4 … etc. for fundamental, first overtone, etc., t-length or thickness of crystal
plate, Y = Young’s modulus of the crystal, and ρ = density of the crystal.
• The variable condenser C1 is adjusted such that the frequency of the applied AC
voltage is equal to the natural frequency of the quartz crystal, and thus resonance takes
place.
• The vibrating crystal produces longitudinal
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ultrasonic waves of large amplitude. 31
 PIEZO ELECTRIC GENERATOR - Construction

Advantages
• Ultrasonic frequencies as high as 500 MHz can be obtained with
this arrangement.
• The output of this oscillator is very high.
• It is not affected by temperature and humidity.

• Disadvantages
• The cost of piezo electric quartz is very high
• The cutting and shaping of quartz crystal are very complex.

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 Applications of ultrasonic waves

• Echo Sounding – Position of Iceberg, Submarines

• Sound Signaling – Signal to Distant Ship
• Depth Sounding - Depth Of Sea
• Cleaning and Removing Dirt
• NON DESTRUCTIVE TESTING –
• Thickness Measurement
• Flaw detection

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 NON DESTRUCTIVE TESTING

• Nondestructive testing is a method of finding defects in an object

without harming the object.
How is ultrasound used in NDT ?
• Sound with high frequencies, or ultrasound, is one method used in NDT.
• Ultrasonic waves are used to detect the presence of flaws or defects
in the form of cracks, blowholes, porosity, etc., in the internal
structure of a material.
• Basically, ultrasonic waves are emitted from a transducer into an object
and the returning waves are analyzed. If an impurity or a crack is
present, the sound will bounce off of and be seen in the returned signal.
• There are two methods of receiving the ultrasound waveform:
– attenuation (or through transmission) and
– reflection (or pulse-echo)
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 NON-DESTRUCTIVE TESTING - TRANSMISSION METHOD
• In attenuation (or through-transmission) mode, a transmitter sends an
ultrasound through one surface, and a separate receiver detects the amount that
has reached it on another surface after traveling through the medium.
• Imperfections or other conditions in the space between the transmitter and
receiver reduces the amount of sound transmitted, thus revealing their
presence.
• Two transducers located on opposing sides of the test specimen are used. One
transducer acts as a transmitter, the other as a receiver.
• A probe on one side of a component transmits (T) an ultrasonic pulse to a
receptor (R) probe on the other side.
• Discontinuities in the sound path will result in a partial or total loss of sound
being transmitted and indicated by a decrease in the received signal amplitude.
Also, the absence of a pulse coming to the receiver indicates a defect.
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 TRANSMISSION METHOD

Sample
Supporting
Surface

Ultrasonic Wave
Generator Transducer

1 PPW 2 36
 Thickness Determination

• Ultrasonic thickness measurement (UTM) is a method of performing non-

destructive measurement of the local thickness of a solid element based on the
time taken by the ultrasound wave to return to the surface. This type of
measurement is typically performed with an ultrasonic thickness gauge.
• Ultrasonic waves have been observed to travel through metals at a constant
speed. Thus, one can calculate the length of the path traversed by the wave using
this formula
T = 𝑣. 𝑡/2
where
T: is the thickness of the sample

v: is the velocity of ultrasound in the given sample

t: is the traverse time

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 Numerical

1 𝑌
𝑓=
2𝑡 𝜌

𝑇 = 𝑣. 𝑡/2

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 Numericals
• A loud speaker emits energy equally in all directions at the rate of 1.5 joules/sec.
What is the intensity level at a distance of 20 m ? (I0 = 10–6 watt/cm2)

• A cinema hall has a volume of 7500 m3. It is required to have reverberation time
of 1.5 sec. What will be the total absorption in the hall ?

• The volume of a hall is 3398m3 and its total absorption equals 92 m2 of open
window. Entry of people inside the hall raises the absorption by 185 m2. Calculate
the change in the reverberation time.

• A hall of volume 5000 m3 has a reverberation time of 3 sec. The surface area of
the sound absorbing surface is 3500 m2. Calculate the average coefficient of
absorption.

• A window, whose area is 1.4 m2, opens on a street where the street noise result in
an intensity level (at the window) of 80 deciBels. How much acoustic power
enters the window via the sound wavesPPW? Given : I0 = 10–12 watt/m2. 39