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Unformatted text preview: 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. ____________________________________________________________________________________________ 3 . SSM REASONING AND SOLUTION Consider the situation in Figure 17.3. If you walk along a line that is perpendicular to the line between the speakers and passes through the overlap point, you will always be equidistant from both speakers. Therefore the sound waves along this line always overlap exactly in phase. Hence, you will always hear the same loudness; you will not observe the loudness to change from loud to faint to loud. On the other hand, if you walk along a line that passes through the overlap point and is parallel to the line between the speakers, your distance from the two speakers will vary such that the difference in path lengths traveled by the two waves will vary. At certain points the path length difference between the two sound waves will be an integer number of wavelengths; constructive interference will occur at these points, and the sound intensity will be a maximum. At other points, the path length difference between the two sound waves will be an odd number of half-wavelengths [(1/2) ,(3/229 , (5/229 , etc.]; destructive interference will occur and the sound intensity will be a minimum. In between the points of constructive and destructive interference, the waves will be out of phase by varying degrees. constructive and destructive interference, the waves will be out of phase by varying degrees....
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- Spring '07