A pair of sound wave sources interfere destructively at a point that is 3/4 of the way from one speaker to the other.If the speed of sound is 343 m/s,and the sound waves are emitted at 880 Hz,which of the following is a possible distance between the two speakers?
A) 2.7 m
B) 0.58 m
C) 1.16 m
D) 1.9 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.

A Pair of Sound Wave Sources Interfere Destructively at a Point