Minimum Distance Between Two Sound Sources

[e(ho0n3]

[SOLVED] Minimum Distance Between Two Sound Sources

Homework Statement

Two sources of sound face each other and emit sounds of equal amplitude and equal frequency but are 180 degrees out of phase. For what minimum separation of the two speakers will there be some point at which (a) complete constructive interference occurs and (b) complete destructive interference occurs

Homework Equations

None. However, I am told that "destructive interference occurs at any point whose distance from one source is greater than its distance from the other source by exactly k/2 wavelengths where k is a positive odd integer (assuming the sound waves from the two sources have the same frequency and are in phase)."

The Attempt at a Solution

Let d be the distance between the two source. If d = 0, I'm thinking that complete destructive interference would occur since the sound waves are out of phase by 180 degrees (hence one wave would cancel the other by superposition). That answers (b). If I let d = 1/2 the wavelength, then when a wave from one source hits the other source, there should be constructive interference right? That should answer (a).

 

[denverdoc]

I'd be inclined to agree if 0 distance is allowed, otherwise it would be lambda for b). In any event you have the concept down, and since question is posed in terms of frequency, just need to convert the answer to terms of frequency.

 

[e(ho0n3]

Thanks. Let f be the frequency and v the velocity of sound. Then,

(a) 1/2 v/f
(b) 0