Two in-phase speakers 2.0 m apart in a plane are emitting 1800 Hz sound waves in

Question

Two in-phase speakers 2.0 m apart in a plane are emitting 1800 Hz sound waves into a room where the speed of sound is 340m/s . Is the point 4.0m in front of one of the speakers, perpendicular to the plane of the speakers, a point of maximum constructive interference, perfect destructive interference, or something in between? pick one of those 3 and say why: 1) This is the point of maximum constructive interference. 2)This is the point of perfect destructive interference.This point is something between maximum 3)constructive interference and perfect destructive interference.

Explanation / Answer

Find the wavelength of the sound: lambda = c/f Find the path-length difference to the point from the two speakers, and divide it by the wavelength. L1 = 4 m L2 = sqrt(4^2+2^2) m deltaL = L2-L1 x = deltaL/lambda If the result is nearly an integer, the waves reinforce at the point. If it is nearly an integer + 0.5, the waves interfere destructively at the point. If it is neither, the point is "something in between". Solving, x = (sqrt(4^2+2^2)-4)/(340/1800) = 2.49954, very close to 2.5, an integer + 0.5. So it's a point of destructive interference.

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