Engineering Acoustics Lecture 3

7/28/2019 Engineering Acoustics Lecture 3

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Chapter 2 . . .


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Frequency analysis of sound

Most sounds contain a combination of many

different frequencies.

The frequency analysis of sound is essential for

noise control. Because sound absorption is

frequency dependent.

i.e. The same material absorb different amounts

of sound energy at different frequencies.

e.g. To choose the proper kind of absorber.


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Frequency analysis of sound . . .

Frequency analysis is performed by measuring theoutput of a sound level meter through a band filter,

which passes only a particular frequency range

between f1 and f2. This is called the bandwidth f

(or pass band).

f = f1 f2, if f1 > f2

where f1, f2 cut-off frequencies


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The centre frequency

fm =f1f2

It is usually convenient to measure and analyze sound in

ranges of frequencies such as the octave. An octave bandis the range of frequencies between any one frequency

and double that frequency. (i.e.f1=2 f2)

e.g. 75 150 Hz, 150 300 Hz, 300 600 Hz, 600 1200 Hz, 1200

2400 Hz, 2400 4800 Hz, 4800 9600 Hz


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Mostly it is sufficient to know the magnitude of the

sound contains within the octave bands. The

preferred center frequencies of acoustic

measurements are;

31.5 Hz, 63 Hz, 125 Hz, 250 Hz, 500 Hz, 1000 Hz, 2000 Hz, 4000Hz, 8000 Hz for octaves.

Frequency analysis of sound is performed using

frequency analyzers such as octaveband analyzer

and 1/3 octave-band analyzer.

Note: 1/3 octave band is obtained by dividing the octave

bandwidth into 3 equal parts.


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Example

A certain noise was analyzed into octave bands. The sound

levels measured in each center frequency are given below.Calculate the combined sound level?

Center frequency (Hz) sound level dB (A)

31.5 60

63 60

125 65

250 70

500 65

1000 65

2000 45

4000 40


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Answer

L = 10 log(106.0+106.0+106.5+107.0+106.5+106.5+104.5+104.0)

= 67.9

= 68 dB (A)


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Measurement conditions

The measurement of sound is done under the following

standard conditions.

1) Free field

2) Reverberant field

3) Semi reverberant field

4) Anechoic field

5) Semi anechoic field

6) Diffuse sound field


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Measurement conditions . . .

1) Free field

This is completely open space where there are no sound

reflections or other modifying factors present.

ReceiverSource


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2) Reverberant field

In a reverberant field the sound energy at any pointis the sum of that directly radiated from the sourceand sound levels reflected from adjacent surfaces.


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Ei = Er + Et + Ea

In a fully reverberant field all the sound energy

striking the bounding surfaces is reflected without

loss. This simplifies that the bounding surfaces

should be highly reflective.

Ei Er

Et

Ea


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3) Semi reverberant field

In a semi reverberant field the prevailing

conditions may be anywhere between free field

and reverberant field conditions.

4) Anechoic field

All the sound measured comes directly from thesource. (All incident energy striking the walls is fully

absorbed)


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5) Semi anechoic field

In a semi anechoic field the sound source is mounted

above a hard reflective surface.


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Note:

The measurements taken outdoors can be considered

to approximate to free field condition. And show

reasonable agreement with anechoic measurements

provided there is no reflective surfaces nearby.

Measurements taken indoors can be considered as

approximating to diffuse field condition. And show

reasonable agreement with reverberant fieldmeasurements.


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6) Diffuse Sound Field

A room is assumed to be completely diffused (Any

closed space is referred to as a room). This means:

1) the acoustical energy is uniformly distributed

throughout the entire room

2) at any point the sound propagation is uniform

in all directions


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Noise Rating

1) Steady noise

2) Time varying noise


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Noise Rating1) Steady noise

When a sound level meter reading fluctuates within arange of less than 5 dB when using the weighting S

then the noise can be treated as steady.

For the measurement of steady noise A-weightingsimple sound level meter is used.

The average value is taken as the reading,

; n total number of readings

}{0

10Ln

10L2

10L1

0

In

10................10(10I10log

L


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Noise Rating . . .

2) Time Varying Noise

The level of many noise varies with time.

e.g. traffic noise, impulse noiseetc

For the measurement of such noise an integrating

sound level meter is used.

It automatically calculates and indicates the value ofequivalent continuous sound level (Leq) for a given time

interval T together with the value of T.


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Equivalent continuous sound level

LAeq,T -> Equivalent Continuous A weighted sound level

within a specified time interval, T.

This is defined as

Where P(t) is the instantaneous A weighted soundpressure.

T = t2 t1


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Equivalent continuous sound level . . .

This is the sound level in dB (A) of a

continuous steady sound which has the same

A-weighted sound energy within a specified

time interval , T as the fluctuating sound

being measured.


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e.g.

Suppose;

sound level L1 acts during time t1,

sound level L2 acts during t2,

sound level L3 acts during t3,

..

sound level Ln acts during tn.

Let T = Total time over which the LAeq,T is required.

T = t1 + t2 + t3+ + tn


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10L1x10II

01

Let

=>

)(0

11

I

I10logL

}{T

10t................10t10t10log

10Ln

n

10L2

2

10L1

1

}{TI

tI........tItI10log

0

nn2211TAeq,

L


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Example

Calculate LAeq,8 over an eight hour period for a

worker exposed to the following noise levels and

duration.

Noise Level dB (A) Duration (hours)

94 2

89 3

98 0.583 2.5


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Answer

LAeq,8 = 91.4 dB (A)

}{8

2.5x100.5x103x102x1010log1083109810891094

Aeq,8L

}{T

10t................10t10t10log10

Ln

n

10L2

2

10L1

1TAeq,

L


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Personal Daily Noise Exposure Level

The equivalent continuous A weighted sound level

over an 8 hour period is called personal daily noiseexposure level, according to the Noise at Work

Regulations, 1989.

This is used for assessing noise exposure in the work

place.

In the regulations recommended level foroccupational noise is a personal daily noise

exposure level of 85 dB (A).


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Personal Daily Noise Exposure Level . . .

i.e. 1st action level is 85 dB (A)

This is taken as the industrial first action levelfor occupational noise.

The second action level is 90 dB (A).

Above this value it is possibly hazardous and earprotection (muff or plugs) must be provided to the

workers or change their work shifts.

A 12 hour LAeq,T value of 75 dB (A) is the common

limit for construction site noise.

Above this level site operations can be stopped by

legal action


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Example

What is the maximum time for which an employee

may spend in a particular work shop where thenoise level is 106 dB (A) without using ear

protection if his noise dose is not to exceed an

equivalent continuous noise level of 90 dB (A) over

the period of 8 hour work shift?

Assume that for the rest of the shift the employee is

subjected to a constant sound level of 85 dB (A).


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Answer

Let t be the required time.


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Example

The noise of a construction site is caused by the following.

Source dB (A) Duration (hrs)

Compressor 89 8

Excavator 85 2

Truck 78 6

Pump 76 7

Calculate the equivalent continuous sound level

over a 12 hour working day of a worker exposed to

the above noise levels.


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Answer

L = 10 log


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Noise exposure from single discrete events

In many situations the total noise exposure over

a period of time is made up from a number of

different individual events such as passing of an

air craft over head or a train near by or a short

bursts of machinery noise.

The measurements of noise from different

events will be made over different durations.


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Noise exposure from single discrete events

For comparison of different types of events itwould be convenient if the equivalent

continuous sound level is averaged over the

same duration.


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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 3