A pair of speakers emits coherent sound waves at a frequency of 440 Hz.A microphone is placed such that it is 1.0 m from one speaker on a line that is perpendicular to the line between the speakers.Which of the following distances reflects a possible distance between the speakers if there is complete destructive interference at the location of the microphone? The speed of sound is 340 m/s.
A) 1.0 m
B) 0.77 m
C) 2.16 m
D) 1.3 m
E) 1.77 m

Question

Quizplus · Accepted Answer

For complete destructive interference, the distance between the two speakers must be an odd multiple of half the wavelength. The wavelength of the 440 Hz sound wave can be found using the formula λ = v/f, where v is the speed of sound and f is the frequency. Plugging in the values, we get λ = 340/440 = 0.773 m. 
Half of the wavelength is 0.3865 m. For complete destructive interference, the distance between the speakers and the microphone along the perpendicular line must be equal to an odd multiple of half the wavelength. 
So, the possible distance between the speakers is 2(0.3865), 6(0.3865), 10(0.3865), and so on. 
Of the given answer choices, only C (2.16 m) is equal to 6 times half the wavelength, so it is the correct answer.

A Pair of Speakers Emits Coherent Sound Waves at a Frequency