Two speakers that are 12.0 m apart produce in-phase sound waves of frequency 245

Question

Two speakers that are 12.0 m apart produce in-phase sound waves of frequency 245 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.

(a) Why is this constructive interference?

(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

L = 12.0 m, f = 245 Hz, v = 340 m/s, so = v/f = 1.388 m,

a) path difference = L/2 - L/2 = 0

b) path difference = (L/2 + x) - (L/2 - x) = 2x = /2, so x = /4 = 3.47 m

c) path difference = (L/2 + x) - (L/2 - x) = 2x = , so x = /2 = 6.94 m

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