Engineering Acoustics Lecture 1

7/28/2019 Engineering Acoustics Lecture 1

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ENGINEERING ACOUSTICS


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Introduction

Acoustics is the science ofsound 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 ofvibrations.


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Example : when a tuning fork is plucked

Air layers are disturbed

and are not in normal

atmospheric pressure

(10-5 Nm-2)

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

compressions and rarefactions.

At compression - Air Pressure (>10-5 Nm-2)

At rarefaction - Air Pressure (


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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.


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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


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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.


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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


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Speed of sound . . .

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

m/s

m/s

331.5 m/s speed at 0 C at 1 atmGenerally 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,

EYoungs Modulus - Density of the medium


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Sound Intensity (I)

Sound intensity is a measure for acoustic energy carried by the

wave.

The acoustic energy passing through unique cross sectional area

taken normal to the direction of sound propagation is called the

sound intensity.

I =

=


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Sound Intensity (I) . . .

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

to the direction of propagation of a plane wave.

The plane atxis displaced by dxin time dt

Intensity of wave I = = = P = Pv

P sound pressure acting on the plane at x

v particle velocity

dxx

F

A=1m2


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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.


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Acoustic Impedance (Z) . . .

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

of infinite extent

Z = C (2) where, Cspeed of sound

- average intensity of the mediumI = Pv (3)

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

I = C v2 I =

For a given medium C is constant.Acoustic intensity I v2 or I P2


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Threshold of Hearing

This is the minimum acoustic energy needed for a normal

person to start hearing.When measured as acoustic pressure it is 2 x 10-5 Nm-2

Sound intensity

I = = 10-12 Wm-2 ;C = 410

Threshold of pain

This 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

I = = 1 Wm-2


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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


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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.


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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 = 10-12Wm-2

Sound Pressure Level (L)

SPL = P sound pressure inNm-2

P0- sound pressure at threshold of hearing

( I P2 => = )

P0 = 2 x 10-5 Nm-2


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

energy emitted per unit time.

LW of a sound source is defined as,

LW =

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


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Answer:

SIL = 10 log SPL = 20 log

At the threshold of hearingSIL = 10 log SPL = 20 log

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

= 0 dB = 0 dB

At threshold of pain

SIL = 10 log SPL = 20 log

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

= 120 dB = 120 dB


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For a plane wave the magnitude of sound intensity

level is same as the sound pressure level in the

audible range. Therefore sound intensity level andsound pressure level can be referred to as Sound

Level.


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2. Measurement of sound

The instrument used is the sound level meter. An omni-

directional microphone converts the sound pressure into avoltage.

This is amplified and passed through a frequency weighting

network which approximates to the ears characteristics and

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.


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Frequency weighting

The frequency weighting network approximates the

frequency responds of the ear.

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Engineering Acoustics Lecture 1