Engineering Science for

Construction B

Chapter 2B

SOUND

1
 Nature of Sound
• Sound is a sensation produced in the ear by
variations in air pressure.
• The pressure variations transfer energy from
sources of vibration.
• A vibration object compresses adjacent
particles of air as it moves in one direction
and leaves them spread out as it moves in
the other direction.
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• Sound waves are longitudinal in type
because the particles of the medium
carrying the wave vibrate in the direction of
travel of the wave.
• Sound wave can travel through solids,
liquids and gases, but not through a vacuum.

3
 Relationship between Velocity,
Wavelength and Frequency
• Wavelength λ (m): distance between any
two repeating points on a wave
• Frequency f (Hz): number of cycles of
vibration per second
• Velocity v (m/s): the distance moved
per second in a fixed direction

4
 v = f
• For every vibration of sound source the
wave moves forward by one wavelength.
The number of vibrations per second
therefore indicates the total length moved in
1 second which is the same as velocity.

5
 Example
• A particular sound wave has a frequency of
440 Hz and a velocity of 340 m/s. Calculate
the wavelength of this sound.

6
 Velocity of Sound
• Velocity of sound depends on the properties
of material through which it is travelling.
• Velocity in air increases as the temperature
or humidity increases.
• Unaffected by variations in atmospheric
pressure and frequency.
• Sound travels faster in liquids and solids
than it does in air.
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Velocity of Sound in Common
Building Materials
Materials Velocity (m/s)
o
Air (0 C) 331
Air (20oC) 344
Water 1498
Timber 3500
Concrete 3700
Steel 5200
Glass 5300
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 Sound Intensity
• Physical quantity.
• the rate of flow of energy through unit area
perpendicular to the direction of travel of
the sound at the place in question.
• Measured in watts per square metre (W/m2)

9
 Loudness
• A subjective sensation (I.e. it depends on
the listener).
• Determined by the intensity of the sound
and by the sensitivity of the observer’s ear.
• Depends upon the frequency as well as the
amplitude of the sound wave.
• Human hearing is not equally sensitive at all
frequencies and tones of different frequency
will be judged to be of different loudness.
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 Relationship between Intensity,
Loudness and Amplitude
• The intensity and loudness of a sound are
directly proportional to the square of the
amplitude of vibration of the sound wave.

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 Threshold of Audibility
(Threshold of Hearing)
• Weakest sound the average human ear can
detect.
• Intensity of threshold of hearing Io=10-12
W/m2.
• Pressure of threshold of hearing po=20x10-6
Pa.
• Because of the change in sensitivity of the
ear to different frequencies, the values
stated are those for a sound frequency of
1000 Hz. 12
 Sound Levels
• Sound Power (P) is the rate at which sound
energy is produced at the source.
Unit: Watt (W)
• Sound Intensity (I) is the sound power
distributed over unit area.
Unit : W/m2

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 r
I
P

P
I=
4r 2

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 r1 I1
P

r2 I2

2
I1  r2 
=  
I 2  r1 
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Example
3m I1 = 10 W/m2
P

15m I2 = ?

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 Sound Intensity Level (SIL)
• Values of sound intensity are converted to
decibel(dB) by comparing them with the
standard value of threshold of hearing.
• Threshold of hearing - weakest sound the
average human ear can detect.

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  I 
SIL = 10 log10  
 Io 

Where
I : intensity of sound being measured(W/m2)
Io: intensity of threshold of hearing
(10-12 W/m2)

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 Sound Pressure Level (SPL)
• Most practical instruments measure sound
by responding to the sound pressure.
• For practical purposes, the SIL and SPL
give the same value in dB.

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 P
SPL = 20 log10  
 Po 

Where
P : pressure of sound being measured(Pa)
Po: pressure of threshold of hearing
(20 x10-6 Pa)

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 Example
A sound has a pressure of 4.5 x 10-2 Pa when
measured under certain conditions.
Calculate the SPL of this sound.

21
 Example
Calculate the change in sound level when the
intensity of a sound is doubled.

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 Classwork
1. A certain sound has an intensity of 3.16 x
10-4 W/m2. Calculate the sound intensity
level in dB if the threshold of hearing
intensity is 10-12 W/m2.

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 Sound Transfer
(a) Airborne Sound

• Travels through air before reaching a

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 (b) Impact Sound

• Generated on a partition
• footsteps, noisy pipes and vibrating
machinery

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 Sound Level Meter
• The meter converts the variations in air
pressure to variation of voltage which are
amplified and displayed on an electrical
meter calibrated in dB.

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 Sound Insulation
Reduction of sound energy transmitted into an
adjoining airspace. Most useful method for
controlling noise in building.

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 Sound Reduction Index
(SRI)

A measure of the insulation against the direct

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 Transmission Coefficient (T)
T = transmitted sound energy /
incident sound energy

1
SRI = 10 log10  
T 

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 Partition

100% 0.01%

Incident Transmitted
Sound Energy Sound Energy

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 For a composite partitions
T1 A1 + T2 A2 + T3 A3
To =
A1 + A2 + A3

Where
To = overall transmission coefficient
T1 = transmission coefficient of one
component

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A1 = area of that component

1
SRI = 10 log10  
 To 

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 Example
At a certain frequency a wall transmits 1% of
the sound energy incident upon it. Calculate
the sound reduction index of the wall at this
frequency.

33
 Example
A wall of 5 m x 2 m contains a window of
area 2 m2. The SRIs are : 50 dB for the
brickwork and 18 dB for the window.
Calculate the overall SRI for the wall.

34
 Classwork
1. 800 units of sound energy are incident upon
a wall and 10 of these units are transmitted
through the wall. Calculate the SRI of this
wall.
2. If a window has a SRI of 33 dB then
calculate the transmission coefficient of this
window.

35
3. An external brick cavity wall is to be 4 m
long and 2.5 m high. The wall is to contain
one window 1.2 m by 0.8 m and one door
0.75 m by 2 m. The relevant SRIs are :
brickwork 53 dB; window 25 dB; door 20
dB. Calculate the overall SRI of the
complete partition.

36
 Sound Absorption
A reduction in sound energy reflected from a
surface; little effect on noise control but
important on sound quality.

Incident Sound
Absorbed
Sound

Reflected Sound
Surface
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Absorption Coefficient ( ) of a surface
= Absorbed sound energy /
Incident sound energy

Absorption of a surface (A)

Total Absorption
= Sum of ( Area x Absorption coefficient)

38
 Reverberation 反響/混響
• The continuing process of an audible sound
after the source of the sound has been
stopped;
• caused by multiple reflections between the
surfaces of a room.

39
 Reverberation Time
• The time taken for a sound to decay by 60
dB from its original level.
• Depends on
1. Absorption at surfaces
2. Frequency of sound
3. Distance between surfaces of room

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• Speech t 1 second
clarity of speech

• Music t 1 second
enhance quality of music

41
 Sabine’s Formula
0.16V
t=
A
Where
t : reverberation time (s)
V : volume of room (m3)
A : total absorption of room surfaces

42
 Example
A hall has a volume of 5000 m3 and a
reverberation time of 1.6 s. Calculate the
amount of extra absorption required to
obtain a reverberation time of 1 s.

43
 Example
A lecture hall with a volume of 1500 m3 has
the following surface areas and finishes and
absorption coefficients (500 Hz).
Walls, plaster on brick 400 m2 (0.02)
Floor, plastic tiles 300 m2 (0.05)
Ceiling, plaster board 300 m2 (0.10)
Calculate the reverberation time at 500 Hz of
this hall when it is occupied by 100 people
(0.46 each)

44
 Classwork
If the reverberation time required for the hall
in the above example is 1.2 s. Calculate the
area of acoustic tiling needed on the walls
to achieve this reverberation time.
(Absorption coefficient of tiles = 0.4 at 500
Hz)

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