Two speakers that are 10.0 m apart produce in-phase sound waves of frequency 265

Question

Two speakers that are 10.0 m apart produce in-phase sound waves of frequency 265 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.

1. What does she hear, constructive or destructive interference?

2. Why?

3. 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?

4. How far from the center must she walk before she first hears the sound maximally enhanced?

Explanation / Answer

apply waveLength L = V/f

L = 340 /265

L = = 1.28m

path diff = (x1-X2) = L/2 = 0.64 m

now if the waves are L/2 out of step they will produce a minimum. thus this produces Destructive interferecne

So she must walk towards one speaker 1.28/2 = 0.64 m

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so that the path difference of the waves reaching her one ear is 0.654 m ( L/2)

Likewise to hear a loud noise the waves must be a full wavelength out of phase

thus (x2-x1) = (5+x - 5-x) = 0.64

x = 0.32 m
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