Two speakers with opposite phase are positioned 3.5 apart, both pointing toward

Question

Two speakers with opposite phase are positioned 3.5 apart, both pointing toward a wall 5.0 in front of them (see the figure). An observer standing against the wall midway between the speakers hears destructive interference.

Two speakers with opposite phase are positioned 3.5 apart, both pointing toward a wall 5.0 in front of them (see the figure). An observer standing against the wall midway between the speakers hears destructive interference. If the observer hears constructive interference after moving 0.84 m to one side along the wall, what is the frequency of the sound emitted by the speakers?

Explanation / Answer

When the listener moves the distance to one speaker is sqrt(4.5^2 + (1.6-.84)^2) = 4.564m and the distance to the other is sqrt(4.5^2 + (1.6+.84)^2) = 5.119m So the separation distance is 5.119 - 4.564 = 0.5552m Therefore ? = 2*0.5552m = 1.11m Since v = ?f then f = v/? = 343m/s/1.11m = 309Hz

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