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Unless indicated otherwise, assume the speed of

Chapter 16, Problem 33E

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QUESTION:

Unless indicated otherwise, assume the speed of sound in air to be v = 344 m/s. Two loudspeakers, A and B (?Fig. E16.35?), are driven by the same amplifier and emit sinusoidal waves in phase. Speaker B is 2.00 m to the right of speaker A. Consider point Q along the extension of the line connecting the speakers, 1.00 m to the right of speaker B. Both speakers emit sound waves that travel directly from the speaker to point Q. What is the lowest frequency for which (a) constructive interference occurs at point Q; (b) destructive interference occurs at point Q?

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QUESTION:

Unless indicated otherwise, assume the speed of sound in air to be v = 344 m/s. Two loudspeakers, A and B (?Fig. E16.35?), are driven by the same amplifier and emit sinusoidal waves in phase. Speaker B is 2.00 m to the right of speaker A. Consider point Q along the extension of the line connecting the speakers, 1.00 m to the right of speaker B. Both speakers emit sound waves that travel directly from the speaker to point Q. What is the lowest frequency for which (a) constructive interference occurs at point Q; (b) destructive interference occurs at point Q?

ANSWER:

Solution 33E Step 1: (a) constructive interference occurs at point Q; For constructive interference, the path difference must be an integral multiple of wavelengths. For the lower wavelength this would be the longest wavelength, with the path difference equal to the one wavelength, Path difference, = AQ- BQ= 3m - 1m = 2m Wavelength ,= = 2m Speed of sound, v= 344 m/s Using, f = v Substituting v= 344 m/s and = 2m 344 m/s f = 2m fc= 172 Hz

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