A speaker generates a continuous tone of 440 Hz.In the drawing,sound travels into a tube that splits into two segments,one longer than the other.The sound waves recombine before being detected by a microphone.The speed of sound in air is 339 m/s.What is the minimum difference in the lengths of the two paths for sound travel if the waves arrive exactly out of phase at the microphone?
A)0.10 m
B)0.39 m
C)0.77 m
D)1.11 m
E)1.54 m

Question

A speaker generates a continuous tone of 440 Hz.In the drawing,sound travels into a tube that splits into two segments,one longer than the other.The sound waves recombine before being detected by a microphone.The speed of sound in air is 339 m/s.What is the minimum difference in the lengths of the two paths for sound travel if the waves arrive exactly out of phase at the microphone? 
A)0.10 m 
B)0.39 m 
C)0.77 m 
D)1.11 m 
E)1.54 m

Quizplus · Accepted Answer

When the sound waves recombine at the microphone, if they are out of phase, they will interfere destructively, resulting in no sound being detected. For a continuous tone of 440 Hz, the period is T = 1/f = 1/440 seconds. If the path length difference is equal to half the wavelength, λ/2, the waves will arrive exactly out of phase. The wavelength of the sound wave is given by λ = v/f = 339/440 m. Therefore, the path length difference should be:

ΔL = λ/2 = (339/440)/2 = 0.385 m

This means that the longer path should be 0.385 m longer than the shorter path to cause destructive interference. The closest value to this is option B) 0.39 m.

A Speaker Generates a Continuous Tone of 440 Hz