Unless indicated otherwise, assume the speed of sound in air to be v = 344 m/s. Two loudspeakers, A and B, are driven by the same amplifier and emit sinusoidal waves in phase. Speaker B is 12.0 m to the right of speaker A. The frequency of the waves emitted by each speaker is 688 Hz. You are standing between the speakers, along the line connecting them, and are at a point of constructive interference. How far must you walk toward speaker B to move to a point of destructive interference?

Solution 35E Step 1: The path difference is an integer number of wavelengths in constructive interference The path difference is a half -integer number of wavelengths in constructive interference v We have relation = f = 344 688 =0.5 m Step 2: To move from constructive to destructive interference, the path difference must change by 2 If you move a distance x toward speaker B, the distance to be gets shorter by x and the distance to A gets longer by x so the path difference changes by 2x. 2x = 2 x = 4 =0.125 m