Question

Two speakers that are 15m apart produce in phase sound waves of frequency 250Hz in a room where the speed of sound is 340m/s. A woman starts out at the midpoint between the two speakers . The room's walls and ceiling are covered with absorbers to eliminate reflections, and she listens with only one ear for best precision. (a) What does she hear: constructive or destructive interference? (b) she now walks slowly toward one of the speakers. How far from the center must she walk before she first hear the sound reach a minimum intensity? (c) how far from the center must she walk before she first hear the sound maximally enhanced?

Answer 1

a) The woman is in the midway of two speakers. So, her path difference will be:

So, she will hear constructive interference.

b) Suppose the woman walks a distance x from the center. So, her path difference for minima condition will be:

c) Suppose the woman walks a distance x from the center. So, her path difference for maxima condition will be: