Two speakers that are 17.0 m apart produce sound waves of frequency 225 Hz in a

Question

Two speakers that are 17.0 m apart produce sound waves of frequency 225 Hz in a room where the speed of sound is 340 m/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. The speakers are 180 out of phase.

A) What does she hear, constructive or destructive interference? Why?

B) She now walks slowly toward one of the speakers. How far from the center must she walk before she first hears the sound reach a minimum intensity?

C) How far from the center must she walk before she first hears the sound maximally enhanced

Explanation / Answer

A)

since she is at centre, she will hear constructive interference

B)

Lambda = speed of sound /f = 340/225 = 1.51 m

For minima, path difference must be lambda/2

So, she must walk a distance of lambda/4 = 1.51/4 = 0.3775 m

c)

For maxima, path difference must be lambda

So, she must walk a distance of lambda/2 = 1.51/2 = 0.755 m

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