Transcript intensity

Chapter 18 WAVES  II
18.1 Sound Waves
A sound wave in air is a longitudinal wave. The restoring
force for such a wave is due to the pressure of air.
The frequencies of audible sound is in the range from 20
to 20,000 Hz. Frequencies above 20,000 Hz are called
ultrasound and frequencies below 20 Hz are called infrasound.
The intensity of a sound wave is the power transported by
this wave per square meter of wave front; the units of intensity
are W/m2.
Threshold of hearing: At a frequency of 103 Hz, the minimum
intensity audible to the human ear is 1.21012 W/m2.
Intensity level: the intensity of sound in a logarithmic scale.
The unit of intensity level is the decibel (dB); we take an
intensity of 0.4681012 W/m2 as our standard of intensity:
 [intensity in W/m 2 ] 

[intensity level in dB]  10log
 0.468  1012 W/m 2 ] 


The threshold of hearing(1.21012 W/m2) corresponds to 4 dB
and the threshold of pain (1 W/m2) corresponds to 120 dB.
Sound
Intensity level
Rupture of eardrum
160 dB
Jet engine (at 30 m)
130
Threshold of pain
120
Rock music
115
Thunder (loud)
110
Subway train (New York City)
100
Heavy street traffic
70
Normal conversation
60
Whisper
20
Normal breathing
10
Threshold of hearing
4
According to Fourier’s theorem, a sound wave of arbitrary
shape can be regarded as a superposition of harmonic waves. The
relative intensity of the harmonic waves in this superposition
determines the timbre (or quality) of the sound.
White noise, consists of a mixture of harmonic waves of all
frequencies with equal intensities.
The musical notes emitted by a piano or a violin consist of a
mixture of just a few harmonic waves.
Note
Frequency
C
261.7 Hz
C#
277.2
D
293.7
D#
311.2
E
329.7
F
349.2
F#
370.0
G
392.0
G#
415.3
A
440.0
A#
466.2
B
493.0
Middle C:
261.7 Hz
C one octave above:
523.3 Hz
C two octaves above:
1046.6 Hz
18.2 The Speed of Sound
The speed of sound
v  1.40
po
o
For the speed of sound in the condition of temperature 0 C,
po = 1 atm = 1.01105 N/m2, and o = 1.29 kg/m3
v = 331 m/s
Material
v
Air
0 º C , 1atm
311 m/s
20 º C , 1atm
344
100 º C , 1atm
386
Helium, 0 º C , 1atm
965
Water (distilled)
1497
Water (sea)
1531
Aluminum
5104
Iron
5130
Glass
5000-6000
Granite
6000
The measurement of the speed of sound in air:
The wavelengths of the normal modes
1  4 L,
2 
4
L,
3
3 
4
L,
5

Eigenfrequencies
1 
v
,
4L
2 
3v
,
4L
3 
5v
L,
4L

In general,
v
n  n
4L
n  1, 3, 5, 
18.3 The Doppler Effect
18.3.1 Moving observers, source at rest
If an observer is moving
toward a wave source, he will
receive more numbers of wave
in a unit time, vO /. Thus, the
number of received waves in a
unit time is
v  vO
 '  

 
v
v
vO
In the case of an observer moves away from a source, the
frequency he receives is
v  vO
 '  

 
v
v
vO
In together, if an observer is moving toward to and away
from the source, the frequency received is
v  vO
 '

v
18.3.2 Moving source, observer at rest
When the source is
in motion toward a
stationary observer, the
effect is a shorten of the
wavelength.
The wavelength the
observer receives is
' 
v


vs

The frequency is
v
 ' 
v  vs
In an opposite case in which the wave source is moving
away from the observer, the measured frequency is
v
 ' 
v  vs
In general, when the source in motion along the line of
source and observer, the frequency observed by a stationary
observer is
v
 '
v  vs
In both source and observer move through the transmitting
medium
v  vO
 '
v  vs
18.4 Supersonic Speeds: Shock Waves
If a source is moving toward a stationary detector at a
speed equal to the speed of sound, we can predict that the
detected frequency will be infinitely great.
When the speed of the source exceeds the speed of sound,
it is called a shock wave.
The Mach cone:
vt
v
sin  

vS t vS
The Mach number:
vs
v
A photograph of
a projectile fired from
a gun at Mach 2.
Problems:
1. 18-4 (on page 421),
2. 18-29,
3. 18-33,
4. 18-49,
5. 18-51,
6. 18-59.