There are two speakers at the front of the room. Each is outputting a 250Hz pure

Question

There are two speakers at the front of the room. Each is outputting a 250Hz pure tone. For each of the following situations, will you hear constructive interference (a loud noise) or destructive interference (soft or no noise). ? represents the wavelength of the 250Hz tone.

You are 2? away from speaker A; 3? away from speaker B and at the speakers the waves are exactly out of phase.

You are 3? away from speaker A; 2.5? away from speaker B and at the speakers the waves are exactly in phase.

You are 2? away from speaker A; 3? away from speaker B and at the speakers the waves are exactly in phase.

You are 3.5? away from speaker A; 3? away from speaker B and at the speakers the waves are exactly out of phase.

Explanation / Answer

Rule of thumb: for the interference to be constructive, two signals should be in phase. In other words, distance between "test point" and every source should be an integer number of ?. If the sources are out of phase, than it's like one of them is shifted by ?/2.

For destructive interference, the difference in distances has to be odd number of ?/2, i.e. ?/2, 3?/2, 5?/2 etc.

With this knowledge, let's see what happens in case A1.

Two speakers are out of phase - it means that we shift one of them (does not matter which one) by ?/2. Let it be Speaker #2. So we end up with the situation when Speaker 1 is at 2? distance and Speaker 2 is effectively at 2.5? distance. Difference is ?/2 - bingo, this is destructive interference.

Case 2 is now cook-book simple.

Case 3 - again, speakers are out of phase, shift Speaker 2 by ?/2, effective distances become equal, constructive interference.

And so on

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