Engineering Acoustics Lecture 2

7/28/2019 Engineering Acoustics Lecture 2

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ENGINEERING ACOUSTICS



Contents

• Introduction

• Measurement of sound

• Sound generation mechanism

• Sound attenuation• Properties of sound

• Room acoustics

• Noise control engineering



Introduction

Acoustics is the science of sound including its production,

transmission and effects.

The effect of sound on engineering is studied under Engineering

Acoustics.

Sound is the sensation that results from variations in the air

pressure.

These pressure fluctuations may take place slowly or rapidly and

are always produced by some source of vibrations.



Example : when a tuning fork is plucked

Air layers are disturbed

and are not in normal

atmospheric pressure

(105 Nm-2)

Sound wave in any medium, consists of a series of alternate

compressions and rarefactions.

At compression - Air Pressure (>105 Nm-2)

At rarefaction - Air Pressure (<105 Nm-2)

A sound wave may be described in terms of variation of air P.



Sound Field: The space in which sound wave travel is called the

sound field.

In a sound field the particles of the medium show a repetitive

movement backwards and forwards about their mean position

Dirn of Propagation: The direction of motion of the particles

is same as the dirn of propagation of the wave.

Therefore it is a longitudinal wave motion.

The velocity of the motion of the particles of the medium iscalled the “particle velocity” ‘v ’.



Fundamentals & Basic Terminology

Sources of sounda. Point source

b. Line source

c. Real source

Speed of sound

Sound Intensity

Acoustic Impedance

Threshold of Hearing

Threshold of Pain

Hearing of Sound

Sound Intensity LevelSound Pressure Level

Sound Power Level



Sources of Sound

a. Point Source

A sound source whose dimension is relatively small

compared to the wavelength is called point source.

It generates spherical

wave fronts. i.e. Crests &

troughs lie on concentric

spherical surfaces.

The sound energy is

emitted equally in all

directions in free space.

Wave fronts representing crests

Wave fronts representing troughs



Sources of Sound . . .

b. Line Source

A line source generates plane wave fronts.

A plane wave propagates only in one direction.

i.e. all crests and troughs lie in one plane.



Sources of Sound . . .

c) Real Source

It has a finite size.

It may radiate different amounts of sound in different

directions.

It can be considered as a point source when the source is

located from an observer at a sufficiently large distance

compared to the size.

Then the sound waves can be treated as plane waves.



The speed of sound ‘C’ in a fluid is given by

k – Bulk Modulus

- Density of the fluid

For a gas, the speed of sound ‘C’ is given by,

k = P,

- is a constant

P – Pressure variation

Speed of sound



Speed of sound . . .

Since the density varies with temperature, at t C speed C is given

by,m/s

m/s

331.5 m/s – speed at 0 C at 1 atm

Generally 340 m/s is used as the speed of sound at normal temperature. Theeffect due to humidity is negligible.

In a solid ‘C’ is given by,

E – Young’s Modulus - Density of the medium



Sound Intensity (I)

Sound intensity is a measure for acoustic energy carried by the

wave.

The acoustic energy passing through unit cross sectional area

taken normal to the direction of sound propagation in unit time is

called as sound intensity.

I =

=



Sound Intensity (I) . . .

Consider a tube of unit cross sectional area with its axis parallel

to the direction of propagation of a plane wave.

The plane at x is displaced by dx in time dt

Intensity of wave

dxx

F

A=1m2

I = = = P = Pv

P – sound pressure acting on the plane at x

v – particle velocity



Acoustic Impedance (Z)

In general, impedance is defined as the ratio between the

action and effect. (Effect is produced by an alternating actionat a point)

Impedance =

In an electrical circuit, In case of sound,

Z = Z = (1)

The sound pressure P is the action and it produces a particle

velocity v.Since P is over unit area Z is called the specific acoustic

impedance.

This has a specific value for the medium and therefore is called

Characteristic impedance.



Acoustic Impedance (Z) . . .

For a given medium , C are constants.

Acoustic intensity I v2 or I P2

Z = ρC (2)

I = Pv (3)

It can be proved that for a plane wave in a homogeneous

medium of infinite extentwhere, C – speed of sound

- average density of the medium

(1),(2) & (3) =>

I = C v2



Threshold of HearingThis is the minimum acoustic energy needed for a normal personto start hearing.

When measured as acoustic pressure it is 2 x 10-5 Nm-2

Threshold of painThis is the maximum acoustic energy a normal person can

tolerate without a pain in ear.

When measured as acoustic pressure it is 20 Nm-2

Sound intensity



Hearing of sound

The following three factors must be in the correctrange for a normal person to hear a sound.

1.Frequency

20 Hz 20 kHz

Infrasonic Audible range Ultrasonic

2.Pressure

2 x 10-5 Nm-2 20 Nm-2

2.Intensity

10-12 Wm-2 1 Wm-2



Hearing of sound . . .

The audible range varies over a wide range. So it is convenient

to use a logarithmic scale.

The most commonly used logarithmic scale is decibel scale.

Eg:-Consider the set of numbers 10-12, 10-5, 106, 1014

% 10-12 (Smallest no. & is called the reference no.)100, 107, 1018, 1026

Now take log: 0, 7, 18 26

Any quantity measured in the decibel scale is always a ratiorelative to some reference no. Therefore it is common to use

the word “level” whenever any quantity is expressed in decibel.



Sound Intensity Level (L)

SIL is defined as,

I – Intensity of sound in Wm-2

I0 – Intensity of reference sound

Usually I0 is taken as the intensity at the threshold of hearing.

I0 = 10-12 Wm-2

Sound Pressure Level (L)

SPL = P – sound pressure in Nm-2

P0- sound pressure at threshold of hearing

( I P2 => = )

P0 = 2 x 10-5 Nm-2



Sound Power Level (LW)The acoustic power of a sound source is the total acoustic

energy emitted per unit time (W).

LW of a sound source is defined as,

LW = 10 log ( )

Where W0 is the acoustic power of the reference source.For convenience W0 is taken as 10-12 J/s.

Example

Find the sound intensity level & sound pressure level of

the threshold of hearing

the threshold of pain





Example:

Find the sound intensity level & sound

pressure level of

1) the threshold of hearing

2) the threshold of pain



Answer:

SIL = 10 log(I/I0) SPL = 20 log(P/P0)

At the threshold of hearing

SIL = 10 log(10-12/10-12) SPL = 20 log(2x10-5/2x10-5)

= 10 log (1) = 20 log (1)

= 0 dB = 0 dB

At threshold of pain

SIL = 10 log(1/10-12) SPL = 20 log(20/2x10-5)

= 10 log(1012) = 20 log(106)

= 120 dB = 120 dB



Sound Level

For a plane wave the magnitude of soundintensity level is same as the sound pressure

level in the audible range. Therefore sound

intensity level and sound pressure level can be

referred to as Sound Level.



Example

If three identical sounds are added, what is

the increase in sound level in decibels?



Answer:

Increase in sound level = 10 log(3I/I0) – 10log(I/I0)

= 10 log(3)

= 10 x 0.4771

= 4.8 dB

5 dB

Note: Intensities can be added arithmetically

i.e. I = I1+I2

But the squares of individual pressures must beadded.

i.e. P = √(P12+P2

2)



Example

Calculate the average of the sound levels

measured at the operator’s level in a factory:

80 dB, 82 dB, 84 dB, 86 dB and 88 dB.



Answer:

Sound level L = 10 log(I/I0) => I = I0 x 10L/10

Average intensity = (I1+I2+I3+I4+I5)/5

= I0 (10L1/10 + 10L2/10 + 10L3/10 + 10L4/10 + 10L5/10) / 5

= I0 (108.0 + 108.2 + 108.4 + 108.6 + 108.8) / 5

LAV = 10 log {I0 x (108.0 + 108.2 + 108.4 + 108.6 + 108.8)/(5 x I0)}

= 10 log { (108.0 + 108.2 + 108.4 + 108.6 + 108.8) / 5 }

= 84.9 dB

85 dB



Chapter 1

Introduction

Fundamentals & Basic terminology

• Source of sound

• Speed of sound

• Sound intensity

• Acoustic impedance

• Threshold of hearing

• Threshold of pain

• Hearing of sound

• Sound intensity level

• Sound pressure level

• Sound power level



2. Measurement of sound

The instrument used is the sound level meter. An omni-directional microphone converts the sound pressure into a

voltage.

This is amplified and passed through a frequency weighting

network which approximates to the ear’s characteristicsand causes an indicator to respond.

A sound level meter is an instrument which responds to

sound in approximately the same as in the human ear.Practically sound contains a spectrum of different

frequency.



Measurement of sound . . .



Measurement of sound . . .

InsulationSound source

Sound source



Frequency weighting

The frequency weighting network approximates the

frequency response of the ear.

The frequency weighting ‘A’ is regarded as a closeapproximation to the sound level perceived by human

ears.

The measurement taken with the sound level meter

should be identified by the frequency weighting used.

Eg: 90 dB (A)

- dB is the unit

- A is the frequency weighting scale



Frequency weighting . . .

A - Blue



Frequency weighting . . .



Time weighting A sound level meter is provided with time weighting to

accommodate the fact that the sounds encountered inpractice fluctuate.

The sound level meter has Fast (F) and Slow (S) time

weighting characteristics. The time constants for F & S

responses are 125 ms & 1000 ms respectively.

A – time varying quantity

- time constant

Ai – initial value



Time weighting . . .

I – Impulse

in some sound level meters, there is an other

response referred to as Impulse (I). Impulse response

has a time constant of 35 ms.

Slow - For the measurement of steady state noises such as

fans or compressors

Fast - For the measurement of variable or fluctuating

noise levels such as traffic

Impulse - For the measurement of very variable or impact

noise levels



Sound level in terms of frequency & time weighting

LAS Slow, A-weighted Sound Level

LAF Fast, A-weighted Sound Level

LCS Slow, C-weighted Sound Level

LCF Fast, C-weighted Sound Level



Calibration of a sound level meterThis is done by means of a source of known noise level

such as a pistonphone.

Calibration by pistonphone is simple in that there is no

difficulty in positioning the source and meter. The

pistonphone fits over the microphone and produces a

note of 250 Hz at 124 dB.



Correction for background noise

Ambient sound: The reading on the sound level meter shows a

total sound pressure level from many sound sourcessurrounding the mike.

The effect of background noise can be neglected when,

Ldifference

= Lmeasured

– Lbackground

≥ 10 dB

If Ldifference is less than 10 dB, a correction has to be made.

Ldifference dB (A) correction dB (A)

6 to 9 -1

4 to 5 -2

3 -3

< 3 the measurement taken is not reliable



Correction for background noise . . .

The background sound level is defined as the ‘A’

weighted sound pressure level of the residual noise (i.e.the noise remaining when the specific noise source is

suppressed) which is exceeded for 90% of the time. And

it is referred to as L90.

Example:

The ambient noise level of a factory is 92 dB (A) when

one machine is in operation. When the machine isstopped the background noise level is found to be 87.5

dB (A). Obtain the noise level produced by the machine

alone.



Example

Ldifference = Lmeasured – Lbackground

= 92 - 87.5 dB (A)

= 4.5 dB (A)

(4<4.5<5)

So the correction factor = -2 dB (A)

Noise level produced by the machine alone

= 92 -2 dB (A)

= 90 dB (A)





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.

Frequency analysis is performed by measuring the outputof a sound level meter through a band filter, which passes

only a particular frequency range between f 1 and f 2. This

is called the bandwidth Δf (or pass band).



Frequency analysis of sound . . .

Δf = f 1 – f 2, if f 1 > f 2 where f 1, f 2 – cut-off frequencies

The center mid frequency

f m = √f 1f 2

It is usually convenient to measure and analyze sound inranges of frequencies such as the octave.

An octave band is the range of frequencies between any

one frequency and double that frequency. (i.e.f 2=2f 1)

e.g. 75 – 150 Hz, 150 – 300 Hz, 300 – 600 Hz, 600 – 1200 Hz, 1200 – 2400 Hz, 2400 – 4800 Hz, 4800 – 9600 Hz

Mostly it is sufficient to know the magnitude of the sound

contains within the octave bands.



Frequency analysis of sound . . .

The preferred center frequencies of acoustic

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

Frequency analysis of sound is performed usingfrequency analyzers such as octave –band analyzer and

1/3 octave-band analyzer.

Note: 1/3 octave band is obtained by dividing the octavebandwidth into 3 equal parts.



Example

A certain noise was analyzed into octave bands. The

sound levels measured in each center frequency aregiven 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



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



Measurement conditions . . .

1) Free field

this is completed open space where there are no

sound reflections or other modifying factors present

2) Reverberant field

In a reverberant field the sound energy at any point is

the sum of that directly radiated from the source and

sound levels reflected from adjacent surfaces.

Ei = Er + Et + Ea

In a fully reverberant field all the sound energy striking

the bounding surfaces is reflected without loss.




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.

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 the

source. (All incident energy striking the walls is fully

absorbed)




5) Semi – anechoic field

In a semi – anechoic field the sound source is mounted

above a hard reflective surface.

Note: The measurements taken outdoors can be considered toapproximate 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 approximatingto diffuse field condition. And show reasonable agreement with

reverberant field measurements.



f b k



Reference book:

Acoustics and noise control

2nd editionB J Smith, R J Peters and S Owen



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 2