Chapter 22B: AcousticsChapter 22B: AcousticsA PowerPoint Presentation byA PowerPoint Presentation by

Paul E. Tippens, Professor of Paul E. Tippens, Professor of PhysicsPhysics

Southern Polytechnic State Southern Polytechnic State UniversityUniversity© 2007

Objectives: Objectives: After completing After completing this module, you should be able this module, you should be able

to:to:

• Compute intensity and intensity levels of sounds and correlate with the distance to a source.

• Apply the Doppler effect to predict apparent changes in frequency due to relative velocities of a source and a listener.

Acoustics DefinedAcoustics Defined

Acoustics is the branch of science that deals with the physiological aspects of sound. For example, in a theater or room, an engineer is concerned with how clearly sounds can be heard or transmitted.

Acoustics is the branch of science that deals with the physiological aspects of sound. For example, in a theater or room, an engineer is concerned with how clearly sounds can be heard or transmitted.

Audible Sound WavesAudible Sound Waves

Sometimes it is useful to narrow the classification of sound to those that are audible (those that can be heard). The following definitions are used:

• Audible sound: Frequencies from 20 to 20,000 Hz.

• Infrasonic: Frequencies below the audible range.

• Ultrasonic: Frequencies above the audible range.

Comparison of Sensory Comparison of Sensory Effects With Physical Effects With Physical

MeasurementsMeasurementsSensory effects Physical property

Loudness

Pitch

Quality

Intensity

Frequency

Waveform

Physical properties are measurable and repeatable.

Sound Intensity Sound Intensity (Loudness)(Loudness)

Sound intensity is the power transferred by a sound wave per unit area normal to the direction of wave propagation.

Sound intensity is the power transferred by a sound wave per unit area normal to the direction of wave propagation.

PI

A

Units: W/m2

Isotropic Source of SoundIsotropic Source of SoundAn isotropic source propagates sound in ever-increasing spherical waves as shown. The Intensity I is given by:

24

P PI

A r

Intensity I decreases with the square of the distance r from the isotropic sound source.

Intensity I decreases with the square of the distance r from the isotropic sound source.

Comparison of Sound Comparison of Sound IntensitiesIntensitiesThe inverse square relationship means a sound that is twice as far away is one-fourth as intense, and one that is three times as far away is one-ninth as intense.

The inverse square relationship means a sound that is twice as far away is one-fourth as intense, and one that is three times as far away is one-ninth as intense.

I1

I2

r1

r2

1 214

PI

r 2 2

24

PI

r

2 21 1 2 2I r I r

Constant PowerConstant Power PP

2 21 1 2 24 4P r I r I

Example 1:Example 1: A horn blows with constant A horn blows with constant power. A child power. A child 8 m8 m away hears a sound of away hears a sound of intensity intensity 0.600 W/m0.600 W/m22. What is the intensity . What is the intensity heard by his mother heard by his mother 20 m20 m away? What is away? What is the power of the source?the power of the source?

Given: Given: II11 = 0.60 W/m = 0.60 W/m22; ; rr11 = = 8 m, 8 m, rr22 = = 20 m20 m

222 2 1 1 1

1 1 2 2 2 122 2

or I r r

I r I r I Ir r

2

22

8 m0.60 W/m

20 mI

I2 = 0.096 W/m2 I2 = 0.096 W/m2

Example 1: (Cont.)Example 1: (Cont.) What is the power of the What is the power of the source? Assume isotropic propagation.source? Assume isotropic propagation.

Given: Given: II11 = 0.60 W/m = 0.60 W/m22; ; rr11 = = 8 m 8 m

II22 = 0.0960 W/m = 0.0960 W/m22 ; ; rr22 = = 20 m20 m

P = 7.54 W P = 7.54 W

2 2 21 1 12

1

or 4 4 (8 m) (0.600 W/m )4

PI P r I

r

The same result is found from: 2

2 24P r I

Range of IntensitiesRange of Intensities

The hearing threshold is the standard minimum of intensity for audible sound. Its value I0 is:

Hearing threshold: I0 = 1 x 10-12 W/m2

The pain threshold is the maximum intensity Ip that the average ear can record without feeling or pain.

Pain threshold: Ip = 1 W/m2

Intensity Level (Decibels)Intensity Level (Decibels)

Due to the wide range of sound intensities (from 1 x 10-12 W/m2 to 1 W/m2) a logarithmic scale is defined as the intensity level in decibels:

Intensity level0

10logI

I decibels (dB)

where is the intensity level of a sound whose intensity is I and I0 = 1 x

10-12 W/m2.

Example 2:Example 2: Find the intensity level Find the intensity level of a sound whose intensity is of a sound whose intensity is 1 x 101 x 10-7-7 W/mW/m22

..

-7 2

-12 20

1 x 10 W/m10log 10log

1 x 10 W/m

I

I

510log10 (10)(5)

Intensity level: = 50

dB

Intensity level: = 50

dB

Intensity Levels of Common Intensity Levels of Common Sounds.Sounds.

Hearing threshold: 0 dB Pain threshold: 120 dB

20 dB 65 dBLeaves or whisper

Normal conversation

Subway

100 dBJet engines

140-160 dB

Comparison of Two Comparison of Two SoundsSounds

Often two sounds are compared by intensity levels. But remember, intensity levels are logarithmic. A sound that is 100 times as intense as another is only 20 dB larger!

20 dB, 1 x 10-10 W/m2Source A

40 dB, 1 x 10-8 W/m2Source

B

IB = 100 IA

Difference in Intensity Difference in Intensity LevelsLevels

Consider two sounds of intensity levels 1 and 2

2 1 2 12 1

0 0 0 0

10log 10log 10 log logI I I I

I I I I

1 21 2

0 0

10log ; 10 logI I

I I

2 02 1

1 0

/10 log

/

I I

I I 2

2 11

10logI

I

Example 3:Example 3: How much more How much more intense is a intense is a 60 dB60 dB sound than a sound than a 30 30 dBdB sound? sound?

22 1

1

10logI

I

2 2

1 1

I60 dB 30 dB 10log and log 3

I

I

I

Recall definition: x

10log means 10N x N

32 2

1 1

I Ilog 3; 10 ;

I I I2 = 1000 I1

Interference and BeatsInterference and Beats

Beat frequency = f’ - fBeat frequency = f’ - f

f

f’

f f’

+

=

The Doppler EffectThe Doppler EffectThe Doppler effect refers to the apparent change in frequency of a sound when there is relative motion of the source and listener.

vf

Right person hears a higher f due to shorter

Left person hears lower f

due to longer

Sound source moving with vs

Apparent f0 is affected by motion.

General Formula for Doppler General Formula for Doppler EffectEffect

00 s

s

V vf f

V v

Definition of terms:

f0 = observed frequency

fs = frequency of source

V = velocity of sound

v0 = velocity of observer

vs = velocity of source

Speeds are reckoned as positive for

approach and negative for

recession

Example 4:Example 4: A boy on a bicycle moves A boy on a bicycle moves north at north at 10 m/s10 m/s. Following the boy is a . Following the boy is a truck traveling north at truck traveling north at 30 m/s30 m/s. The . The truck’s horn blows at a frequency of truck’s horn blows at a frequency of 500 500 HzHz. What is the apparent frequency . What is the apparent frequency heard by the boy? Assume sound travels heard by the boy? Assume sound travels at at 340 m/s340 m/s..

30 m/s 10 m/s

V = 340 m/s

fs = 500 Hz

The truck is approaching; the boy is fleeing. Thus:

vs = +30 m/svs = +30 m/s v0 = -10 m/sv0 = -10 m/s

Example 4 (Cont.):Example 4 (Cont.): Apply Doppler Apply Doppler equation.equation.

vs = 30 m/s v0 = -10 m/s

V = 340 m/s

fs = 500 Hz

f0 = 532 Hzf0 = 532 Hz

00

340 m/s ( 10 m/s)500 Hz

340 m/s - (30 m/s)ss

V vf f

V v

0

330 m/s500 Hz

310 m/s)f

Summary of AcousticsSummary of Acoustics

Acoustics is the branch of science that deals with the physiological aspects of sound. For example, in

a theater or room, an engineer is concerned with how clearly sounds can be heard or transmitted.

Acoustics is the branch of science that deals with the physiological aspects of sound. For example, in

a theater or room, an engineer is concerned with how clearly sounds can be heard or transmitted.

Audible sound: Frequencies from 20 to 20,000 Hz.

Infrasonic: Frequencies below the audible range.

Ultrasonic: Frequencies above the audible range.

Summary (Continued)Summary (Continued)

Sensory effects Physical property

Loudness

Pitch

Quality

Intensity

Frequency

Waveform

Measurable physical properties that determine the sensory effects of individual sounds

Summary (Cont.)Summary (Cont.)

Sound intensity is the power transferred by a sound wave per unit area normal to

the direction of wave propagation.

Sound intensity is the power transferred by a sound wave per unit area normal to

the direction of wave propagation.

PI

A

Units: W/m2

Summary (Cont.)Summary (Cont.)

The inverse square relationship means a sound that is twice as far away is one-fourth as intense, and one that is three times as far away is one-ninth as intense.

The inverse square relationship means a sound that is twice as far away is one-fourth as intense, and one that is three times as far away is one-ninth as intense.

24

P PI

A r 2 2

1 1 2 2I r I r

Summary of Formulas:Summary of Formulas:

PI

A 2

2 11

10logI

I

Beat freq. = f’ - fBeat freq. = f’ - f 00 s

s

V vf f

V v

v = fv = f

0

10logI

I

0

10logI

I

Hearing threshold: I0 = 1 x 10-12 W/m2 Pain threshold: Ip = 1 W/m2

Hearing threshold: I0 = 1 x 10-12 W/m2 Pain threshold: Ip = 1 W/m2

CONCLUSION: Chapter 22BCONCLUSION: Chapter 22BAcousticsAcoustics