Two speakers are set up along the x-axis. Both are facing to the right (+x) and

Question

Two speakers are set up along the x-axis. Both are facing to the right (+x) and putting out sound at a frequency of 800Hz, with intensity 120 W/m2. They are in phase (both start at a peak). The first speaker is located at the origin. The second is at some negative value of “x” (in meters). Assume the sound travels only along the x-axis, so its intensity will not drop off with distance. You are standing on the positive x-axis. vsound = 344m/s.

a) List two “x” nearest the origin, where the second speaker could be located, so that you would hear sounds of intensity 480 W/m2 and 240 W/m2 respectively.
b) If the second speaker is at the “x” value for 240 W/m2 found in part-a, what initial phase could we give its wave, so that you would hear no sound?
c) If the phase shift you found in part-b is to be achieved by delaying the second speaker, by how much time should it lag the first?

Explanation / Answer

a)
480w/m2 is not possible, because of conservation of energy. (Maximally we can have 240 W/m2)

About 240W/m2:
We must put second speaker in a point that both of speakers be "in phase"

= v/f >>>> = 344/800 = 0.43 m

Therefore we can put second speaker at the origin or -0.43m or +0.43m or -0.86m or +0.86m and .....

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b)
The speakers must be in "anti phase"

Therefore the initial phase of the second speaker must be

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c)

f = 800 Hz, therefore period (T) of the speakers is 1/800 second (0.00125 second)

The speakers must be in "anti phase", therefore second speaker must lag the first speaker by T/2.

T/2 = 0.000625 s = 6.25 * 10^4

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