Chapter 19 Sound waves. 19-1 Properties of Sound waves. 19-2 Traveling sound waves. 19-3 * The speed of sound. 19-4 Power and intensity of sound waves . 19-5 Interference of sound waves. 19-6 * Standing longitudinal waves. 19-7 * Vibrating system and sources of sound.
19-1 Properties of Sound waves
19-2 Traveling sound waves
19-3* The speed of sound
19-4 Power and intensity of sound waves
19-5 Interference of sound waves
19-6* Standing longitudinal waves
19-7* Vibrating system and sources of sound
19-9 The Doppler effect
When we discuss sound waves, we normally mean longitudinal wave in the frequency range 20 Hz to 20,000 Hz, the normal range of human hearing.
For simplification, we will consider the sound wave in 1D case.
In Fig19-2, as the piston (活塞) moves back and forth, it alternately compresses and expands (使稀薄)) the air next to it.
This disturbance travels
down the tube as a sound wave.
Under certain conditions
It is convenient to use density and pressure to describe the properties of fluids.
1) Let us assume that the pistol is driven so that the density and pressure of air in the tube will vary as a sine function.
2) What’s the relationship between and ?
From the definitions of bulk modulus(体模量/膨胀系数) (Eq(15-5)) and density , when m is fixed, we have
3) How to find the displacement of an element of gas inside the tube?
The undisturbed density of is
A is the corss-sectional area.
isthe velocity ofoscillation of an element in fluids.
v= /k isthe velocity of sound wave.
As in the case of thetransverse mechanical wave, the speed of a sound wave depends onthe ratio ofanelastic propertyof the medium and aninertial property. For a 3D fluid,
Note:1) B is the bulk modulus, is the mass density.
2) Use Newton’s law for a system of particles.
As the wave travels, each fluid element exerts a force on the fluid element ahead of it. If the pressure increase in the fluid element is ,
The power delivered bythe element is:
Average over any number of full cycles.
Intensity I: (19-19)
The response of the ear to sound of increasing
intensity is approximately logarithmic.
One can define a logarithmic scale of intensity called the “sound level SL”
Where is a reference intensity, which is
chosen to be (a typical value for the
threshold of human hearing(听觉阈)).
A sound of intensity (听觉阈)has a sound level of 0 dB.
The sound at the upper range of human hearing, called the threshold of pain (痛觉阈) has an intensity of and a SL of 120 dB.
Spherical sound waves are emitted uniformly in all
directions from a point source, the radiated power
P being 25 w. What are the intensity and the sound
level of the sound wave at a distance r=2.5m from the source?
driven from a common source.
At point P the pressure variation
due only to speaker is and
that due to alone is . The
total pressure disturbance at
point P is .
19-5 Interference of sound waves
The type of interference that occurs at point P
depends on the phase difference between the
When ( m=0,1,2,…...) (19-23),
The intensity reaches a maximum value, forming constructive interference.
When destructive interference occurs. The intensity has a minimum value.
We assume a train of
sine waves travels down a tube( Fig19-7).
1) If theend is open,
the wave at the end will behave as a pressure node(波节);
2)If theend is closed, a pressureantinode(波腹) will form at the end.
a).For open end, the longitudinal pressure wave is reflected with a phase change of , because the pressure at the open end must at the value , same as the environment’s.
In this case, it likes the string fixed at both ends.
b).For the closed end, the pressure can vary freely.
c).The superposition of the original and reflected
waves gives a pattern of standing waves.
d).Resonance can happen, when the driving frequencymatches one of the natural frequency of the system, which are determined by the length of the tube (L).
We have already studied the propagation of the sound wave, and now to understand the nature of the sound we must study the vibration system that produces it.
We can classify musical instruments into three categories: those based on vibration string; those based on vibration column of air, and more complex system including plates, rods, and membranes.
ascending order, so that .
The lowest frequency, is called the “fundamental
frequency(基频)”, and the corresponding mode of
oscillation is called the “fundamental mode”. The
higher frequencies are called “overtones(泛音)”, with being the first overtone, the second overtone, and so on. In some systems:
pleasant sounds while others produce harsh (刺耳的) or discordant (不和谐) sounds?
When several frequencies are heard simultaneously, a pleasant sensation results if the frequencies are in the ratio of small whole numbers(整数), such as 3:2 or 5:4.
We have chosen the phase constants to be zero, and same amplitudes.
would perceive a tone
at a frequency .
Since ~ , the amplitude frequency
is small. The amplitude
whenever equals +1 or -1 ,since the
intensity depends on the square of the amplitude.
Each of these values occurs once in each cycle of
the envelope, thus
A violin string that should be tuned to concert A (440Hz) is slightly mistuned. When the violin string is played in its fundamental mode along with a concert A tuning fork, 3 beatsper second are heard. (a) What are the possible values of the fundamental frequency of the string? (b)Suppose the string were played in its first overtone simultaneously with a tuning fork with 880Hz. How many beats per second would be heard? (c) When the tension of the string is increased slightly, the number of beatsper second in the fundamental mode increases. What was the original frequency of the fundamental?
In a paper written in 1842, Doppler (1803~1853)
called attention to the fact that the color of a
luminous body must be changed by relative motion
of the body and the observer. This “Doppler effect”
as it is called, applies to waves in general.
Suppose the source and observer move along the line joining them.
See动画库\波动与光学夹\2-21Doppler Effect A.exe
Fig19-14 shows a source of sound Sat rest and an observer Omoving toward the source at a speed .
If the frequency of wave is f, what is the actually one f ’ heard by the ear?
Because of the motion toward the source, the observer receives additional waves in the same time t.
2. Moving source, observer at rest
In this case, the wavelength is shortenedfrom to .
* When the observer is in motion away from the source,
Is given by
* If the source moves away form the observer, the
frequency heard is
Where the upper signs (+ numerator, -denominator)
correspond to the source and observer moving toward the other and the lower signs in the direction away from the other.
4. If a source of sound is moved away from an
observer and toward a wall, the observer hears
waves reflected from the wall, and this is raised in
pitch. The superposition of these two wave trains
A similar effect occurs if a wave from a stationary
source is reflected from a moving object. The beat
frequency can be used to deduce the speed of the
object. This is the basic principle of radar monitors,
and it is also used to track satellites.
Wavefront when .
Wavefront when .
Predicted in 1924...
E. A. Cornell
C. E. Wieman
A. Einstein S. N. Bose
Extremely low temperature;
The atoms are still in gas state
10-9 K obtained
10-6 K obtained
The siren （警报器）of a police car emits a pure tone at a
frequency of 1125 Hz. Find the frequency that you
would perceive in your car.
(a) your car at rest, police car moving toward you at 29 m/s;
(b) police car at rest your moving toward it at 29 m/s
(c) you and police car moving toward one another at 14.5 m/s
(d) you moving at 9 m/s, police car chasing behind
you at 38 m/s