Two speakers are positioned 5.00 m apart against a wall. An observer standing 8.

Question

Two speakers are positioned 5.00 m apart against a wall. An observer standing 8.00 m away from the wall and midway between the speakers is at a location of constructive interference. (a) Can the person walk forward from the point and encounter a point of destructive interference? Why? (b) By moving 0.54 m to one side of his original position, the observer experiences the first location of destucitve interference. What is the frequency of the sound emitted by the speakers? The answers are (a) always constructive interference and (b) 536.5 Hz. Please show the work, any formulas used, and explain.

Explanation / Answer

a) consider distance x from the centre of the wall
   Now, given the fact that the distance from the middle line is same for two speakers , the person can never ebncounter destructive interference on the centre line
b) Path difference at given location = sqroot((2.5+0.54)^2+8^2) - sqroot((2.5-0.54)^2+8^2) = 0.3215 m = lambda/2 [ for destructive interference]
   now, c = lambda*f
   lambda = 334/f
   so f = 519.39 Hz

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