Final Exam Question for General Physics 1 A continuous tone of 680 Hz is generat

Question

Final Exam Question for General Physics 1

A continuous tone of 680 Hz is generated by a speaker. The 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 340 m/s. What is the minimum difference in the lengths of the two paths for sound travel to produce constructive interference at the microphone?

The answer is 0.5 m.

But why? Please explain in detail because this question is confusing.

The following are some questions that need to be clarified as well:

a. Where they in phase or out of phase to begin with? Why?

b. Is there a maximum difference in lengths of the two paths for sound travel to produce constructive      interference at the microphone? Why?

c. What if the segments were equal lengths?

d. Since the minimum distance for constructive interference in this case is 0.5 m, would the mininmum distance for destructive interference be 0.0 m or 1.0 m? Why?

Thanks.

Explanation / Answer

wavelength = speed of sound/frequency = 340/680 = 0.5 m

To produce constructive interference, the difference in length = k, the minimum difference = = 0.5 m.

a) They begin with in phase, because they start from the same place (loudspeaker).

b) To produce constructive interference, the difference in length = k, where k in an integer. There is no maximum integer, so no maximum difference in length.

c) If the segments are equal length, the difference = 0 = k, where k = 0, so there is a constructive interference at the microphone.

d) To produce destructive interference, the difference in length = (k + 1/2), minimum difference = /2 = 0.25 m

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