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1537 Chapter 16 Superposition and Standing Waves Conceptual Problems 1 [SSM] Two rectangular wave pulses are traveling in opposite directions along a string. At t = 0, the two pulses are as shown in Figure 16-29. Sketch the wave functions for t = 1.0, 2.0, and 3.0 s. Picture the Problem We can use the speeds of the pulses to determine their positions at the given times. 2 Repeat Problem 1 for the case in which the pulse on the right is inverted. Picture the Problem We can use the speeds of the pulses to determine their positions at the given times. 3 Beats are produced by the superposition of two harmonic waves if ( a ) their amplitudes and frequencies are equal, ( b ) their amplitudes are the same but their frequencies differ slightly, ( c ) their frequencies differ slightly even if their amplitudes are not equal, ( d ) their frequencies are equal but their amplitudes differ slightly. Chapter 16 1538 Determine the Concept Beats are a consequence of the alternating constructive and destructive interference of waves due to slightly different frequencies. The amplitudes of the waves play no role in producing the beats. ( ) ) ( and c b are correct. 4 Two tuning forks are struck and the sounds from each reach your ears at the same time. One sound has a frequency of 256 Hz, and the second sound has a frequency of 258 Hz. The underlying hum frequency that you hear is ( a ) 2.0 Hz, ( b ) 256 Hz, ( c ) 258 Hz, ( d ) 257 Hz. Determine the Concept The tone you hear is the average of the frequencies emitted by the vibrating tuning forks; ( ) ( ) Hz 258 Hz 256 2 1 2 1 2 1 av + = + = f f f or 257 Hz. Hence ( ) d is correct. 5 In Problem 4, the beat frequency is ( a ) 2.0 Hz, ( b ) 256 Hz, ( c ) 258 Hz, ( d ) 257 Hz. Determine the Concept The beat frequency is the difference between the two frequencies; Hz 2 Hz 256 Hz 258 beat = = = f f . Hence ( ) a is correct. 6 As a graduate student, you are teaching your first physics lecture while the professor is away. To demonstrate interference of sound waves, you have set up two speakers that are driven coherently and in phase by the same frequency generator on the front desk. Each speaker generates sound with a 2.4m wavelength. One student in the front row says she hears a very low volume (loudness) of the sound from the speakers compared to the volume of the sound she hears when only one speaker is generating sound. What could be the difference in the distance between her and each of the two speakers? ( a ) 1.2 m, ( b ) 2.4 m, ( c ) 4.8 m, ( d ) You cannot determine the difference in distances from the data given. Determine the Concept Because the sound reaching her from the two speakers is very low, the sound waves must be interfering destructively (or nearly destructively) and the difference in distance between her position and the two speakers must be an odd multiple of a half wavelength. That is, it must be 1.2 m, 3.6 m, 6.0 m, etc. Hence ( ) a is correct. ... View Full Document

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