Two speakers, facing each other, produce coherent sound waves that interfere destructively at a point that is ¾ of the way from one speaker to the other. If the speed of sound is 343 m/s, and the sound waves are emitted in phase at 880 Hz, which of the following is a possible distance between the two speakers?
A) 2.7 m
B) 0.58 m
C) 1.56 m
D) 2.3 m
E) 77 cm

Question

Quizplus · Accepted Answer

The distance between the two speakers is equal to the wavelength of the sound wave multiplied by the number of half-wavelengths between the speakers. In this case, the point of destructive interference is ¾ of the way from one speaker to the other, which means that there are 3 half-wavelengths between the speakers. The wavelength of the sound wave is equal to the speed of sound divided by the frequency, which is 343 m/s / 880 Hz = 0.39 m. Therefore, the distance between the two speakers is 3 * 0.39 m = 1.17 m.

Two Speakers, Facing Each Other, Produce Coherent Sound Waves That