CHAPTER
17 THE PRINCIPLE OF
LINEAR SUPERPOSITION AND
INTERFERENCE PHENOMENA
CONCEPTUAL QUESTIONS
____________________________________________________________________________________________
1.
REASONING AND SOLUTION The principle of linear superposition states that when
two or more waves are present simultaneously at the same place, the resultant wave is the
sum of the individual waves. This principle does not imply that two sound waves, passing
through the same place at the same time, always create a louder sound than either wave
alone. The resultant wave pattern depends on the relative phases of the two sound waves
when they meet. If two sound waves arrive at the same place at the same time, and they are
exactly in phase, then the two waves will interfere constructively and create a louder sound
than either wave alone. On the other hand, if two waves arrive at the same place at the same
time, and they are exactly out of phase, destructive interference will occur; the net effect is
a mutual cancellation of the sound. If the two sound waves have the same amplitude and
frequency, they will completely cancel each other and no sound will be heard.
____________________________________________________________________________________________
2.
REASONING AND SOLUTION If you are sitting at the overlap point between the two
speakers in Figure 17.4, the two sound waves reaching you are exactly out of phase. You
hear no sound because of destructive interference. If one of the speakers is suddenly shut
off, then only one sound wave will reach your ears. Since there is no other sound wave to
interfere with this sound wave, you will hear the sound from the single speaker.
____________________________________________________________________________________________
4.
REASONING AND SOLUTION If the width of the speakers is D, then sound of wavelength  will diffract more readily if the ratio  / D is large. Since longer wavelengths
correspond to lower frequencies, we see that lower-frequency sounds diffract more readily
from a given speaker than higher-frequency sounds. Since the frequencies of the sounds of
the female vocalists are higher than the frequencies of the sounds of the rhythmic bass, the
sounds of the female vocalists will not diffract to the same extent as the sounds of the
rhythmic bass. Thus, diffraction allows the bass tones to penetrate the regions to either side
of the stage, but it does not permit the same help to the sounds of the female vocalists.
____________________________________________________________________________________________
5.
REASONING AND SOLUTION When a wave encounters an obstacle or the edges of an
opening, it bends or diffracts around them. The extent of the diffraction depends on the ratio
of the wavelength  to the size D of the obstacle or opening. If the ratio  / D is small, little
diffraction occurs. As the ratio  / D is made larger, the wave diffracts to a greater extent.
In Example 1 in Section 16.2, it is shown that the wavelength of AM radio waves is 244 m,
while the wavelength of FM radio waves is 3.26 m. For a given obstacle, the ratio  / D
will be greater for AM radio waves; therefore AM radio waves will diffract more readily
around a given obstacle than FM waves.
____________________________________________________________________________________________
PROBLEMS
____________________________________________________________________________________________
1.
REASONING AND SOLUTION According to the principle of linear superposition,
when two or more waves are present simultaneously at the same place, the resultant wave is
the sum of the individual waves. Therefore, the shape of the string at the indicated times
looks like the following:
SSM
____________________________________________________________________________________________
2.
REASONING AND SOLUTION The shape of the string looks like
t=1s
t=2s
t=3s
t=4s
0
2
4
6
8
10
12 cm
_____________________________________________________________________________