Chapter 14 Sound
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