Engineering Acoustics Lecture 9

7/28/2019 Engineering Acoustics Lecture 9

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Chapter 5

Properties of Sound . . .


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Sound Transmission through Walls & Partitions

Source side receiving side

Ei incident acoustic energy density

Et transmitted acoustic energy density

Wall / Partition

EtEi

Sound

source


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Sound Reduction Index (R)

The basic property of a partition whichdetermines its effectiveness as a sound insulator

is the sound reduction index / transmission loss.

This term is commonly used to describe sound

insulation.

And it is given by,

; t transmission coefficient of the partition

)t

1(log10R


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Sound Reduction Index (R) . . .

Fraction of the sound energy transmitted,

So,

Note: Sound Energy DensityThe sound intensity of a plane wave, I is the

acoustic energy traveling a distance c through

unit area for 1 s.

)E

E(log10R

t

i

i

t

E

Et


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Example

An exterior wall constructed from brick has anarea 30 m2. In which there is a glass window

10m2. If the sound reduction indices of brick &

glass are 50 dB & 20 dB respectively, calculate

the transmission loss of the composite wall.


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Answer

For brick,Rb = 10 log (Ii / Ib)

50 = 10 log (Ii / Ib)

Ib = 10-5 Ii

For glass.

Rg = 10 log (Ii / Ig)

20 = 10 log (Ii / Ig)

Ig

= 10-2 Ii


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Answer

For composite partition;

299.4log10

}

I)10x10(2x3

1

I{log10R

x1010xI20x10xI30xI

)I/(Ilog10R

i

2-5-

iav

2-

i

5-

iav

aviav


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Mass LawThe mass law gives the average transmission

loss for a diffuse source of sound as a functionof the wall surface weight and the frequency.

The mass law is only a convenient, rough

approximation to the performance of single

walls.

Sound reduction,

R = 20 log (f m ) 43

;ffrequency of incident sound (Hz)

m

mass per unit area (kg / m2

)


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Mass Law . . .

Thus the effectiveness of the sound insulationdepends on the frequency and the mass.

Single leaf construction includes compositeconstruction such as plastered brickwork, as

long as the layers are bonded together (there

should be no air gap between the two).


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Example

Estimate the increase in R when the mass of the

single leaf/partition or frequency is doubled.


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Answer

R1 = 20 log (f m ) 43

R2 = 20 log (2f m ) 43

Increase in sound reduction,

= R2 R1

= 20 log (2)

= 6.0206 dB


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Mass law . . .

A perfect limp panel (one without any structural

stiffness) has an increase in sound reduction of

6 dB for each doubling of mass or frequency.

A normal partition has some stiffness, hence the

increase in sound reduction is 5 dB for each

doubling of mass or frequency.


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Sound Reduction index of a double leaf

wall / partition

For simplicity assume both panels have thesame mass per unit area, m.

Then,

; d width of air gap

R01 sound reduction of a single leaf partition given

byR01 = 20 log (f m) 43

k = 2f / C = 2 /

C

speed of sound in air

(2kd)log202RR 0102


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Wave Propagation in Solids

There are three main types of waves found insolids,

Longitudinal

Transverse

Bending


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Wave Propagation in Solids . . .

Bending waves are flexural waves which can

occur along the length of a partition or a plane.

Bending waves produce large deflections in the structure.

Wall /

partition


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Wave Propagation in Solids . . .

The velocities of bending waves (CB) are frequency

dependent.For flat plates such as a partition it is given by

Where hthickness of the plateffrequency of the bending wave

CLspeed of sound in the solid medium

; EYoungs modulus

- density

LB Cfh1.8C

ECL


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Factors affecting Sound Insulation

The main three factors are,

Resonance

Coincidence effect Flanking transmission


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Resonance

P a particle of the panel (simple harmonic

motion)

Natural frequency of the panel

P

x = a

x = - a

T

1f0


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Resonance . . .Resonance occurs when the frequency of the incident

sound, f = f0 ,(f0 is the natural frequency of the wall)

A drop in sound insulation is observed at resonance.Usually the natural frequencies are low. So,

resonance affects insulation at low frequencies.

S

f

f0


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Coincidence Effect

When a plane wave of wave length is incident on a

wall or a partition at angles other than 900, theirtransmission can be amplified by the flexing inwards

and outwards of the partition.

Wall /

partition


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Coincidence Effect . . .At a certain frequency the amplitude of the

bending vibration becomes comparable to theamplitude of incident wave resulting in a

decrease in sound insulation.

This frequency is called the coincidence

frequency. This phenomenon is called the

coincidence effect.

The coincidence frequency, fis given by

E

sinh1.8

Cf

2

2


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Coincidence Effect . . .The lowest frequency at which coincidence

occurs is called the Critical Frequency.i.e. when sin = 1

At any frequency higher than fc , coincidence

will occur. As a result sound reduction index will

be reduced.

Eh1.8

Cf

2


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Example

Estimate the critical frequency of a 120mm thick

brick wall. The velocity of sound in brick and air

is 2350m/s and 330 m/s respectively.


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Factors affecting sound insulation..

Flanking Transmission:

This occurs when sound is transmitted from one

space to another indirectly, through adjoining

parts of the structure.


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Factors affecting sound insulation..

Flanking Transmission . . .

These indirect paths are called flanking paths.

The expected sound insulation is not achieved due to

flanking transmission.

Successful noise control solutions must address

the possibilities of flanking transmission.


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Reference book:

Acoustics and noise control

2nd edition

B J Smith, R J Peters and S Owen


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Practical schedule

3 Practical

2 - Outdoors

1 Industrial visit

Assignments:

Three (3) in-class assignments, each carry 10 marks.

3 for performance

7 for assignment

Documents

Engineering Acoustics Lecture 9