Question

Two identical loudspeakers, speaker 1 and speaker 2, are 2.0 m apart and are emitting 1700-hz sound waves into a room where the speed of sound is 340 m/s. consider a point 4.0 m in front of speaker 1, which lies along a line from speaker 1, that is perpendicular to a line between the two speakers. is this a point of maximum constructive interference, a point of perfect destructive interference, or something in between?

Answer 1

Given the following in the problem:

Distances : 2.0 m and 4.0 m
Sound waves : 1700 hz
Speed of sound : 340 m/s

Get the wavelength of the sound by using the formula:
Lambda = speed of sound/sound waves
Lambda = 340 m/s / 1700 hz
Lambda = 0.2
Get the path length difference to the point from the two speakers
L1 = 4mL2 = sqrt (42+ 22) m
Delta = 4.47

x = delta / lambda

If the outcome is nearly an integer, the waves strengthen 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 somewhat in in the middle.

Solving x = (4.47 – 4) / (0.2) = 2.35 an integer +0.5 so it’s a point of destructive interference.