Chapter 14

Sound

Characteristics of sound

2

A special and important type of mechanical wave

Speed of sound:

Loudness: related to the energy of sound

,B

v

depends on the medium

Audible range: 20Hz ~ 20000Hz

Pitch: related to the frequency of sound

Infrasonic & ultrasonic

Intensity of sound

3

Sound level: using a logarithmic scale

Unit: decibel (dB)

0

10 logI

I

Loudness: represented by the intensity

2 21/

2I P S v A

Range of ear: 10-12W/m2 ~ 10W/m2 (painful)

I0 = 10-12W/m2

Notice: logarithmic scale 50dB ~ 20dB?

Distance & sound level

4

Example1: Sound from a loudspeaker is measured to be 60dB at a distance of 2m. To obtain a level of 40dB, how can we choose the distance?

Solution: Sound level0

10 logI

I

11 2

2

10 logI

I

1 2100I I

For a spherical wave: 2 21 2 2 1 / /I I r r

Distance we choose: 2 110 20mr r

Doppler effect

5

The change in pitch: speeding car or train

Source moves toward observer → higher

Source moves away from observer → lower

Doppler effect: occurs for all types of waves

For light: red shift → big bang theory

Physical analysis

6

Choose the frame of medium, observer and source move in a straight line, vo and vs are relative to

medium (air), v is the wave speed in the air, and:

f : emitted frequency by the source

f ’ : detected frequency by the observer

1) Observer and source both stay at rest:

vf f

Moving case A

7

2) Observer moving, source stationary:

vo

Extra vo /S

v/

v O

o ov v vvf f

v toward source:

o ov v vvf f

v away from source:

Moving case B

8

3) Source moving, observer stationary:

vs s

S

v

O

s

v vf f

v v

toward observer:

away from observer:

sv v

f

s

v vf f

v v

General case

9

Thinking: Why case A is different from case B?

Change in both wave speed & wavelength:

o

s

v vvf f

v v

Upper sign: moving toward each other

Lower sigh: moving away from each other

c vf f

c v

Doppler effect for light:

Sound of moving car

10

Example2: When a car passes, an observer hears the sound of car changing from 1200Hz to 1000Hz. If the speed of sound is 330m/s, what is the speed of car and the original frequency?

Solution: Toward observer 1200s

vf f

v v

Away from observer: 1000s

vf f

v v

Solving equations:

30 m/s,sv 1091 Hzf

Sound echo

11

Thinking: Someone carrying a loudspeaker moves at speed u to a wall, and hears a sound echo. If the emitted frequency is f, what is the frequency f ’? (Suppose the speed of sound is v)

u uv u

f fv u

Shock wave

12

Source in a supersonic speed

vΔt

S vs

· · ·

vs Δt

shock wave

vs / v : Mach number

sins

v

v