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.
Constructive Destructive You are 3? away from speaker A; 2.5? away from speaker B and at the speakers the waves are exactly out of phase.
Constructive Destructive You are 4? away from speaker A; 5? away from speaker B and at the speakers the waves are exactly in phase.
Constructive Destructive You are 3? away from speaker A; 2.5? away from speaker B and at the speakers the waves are exactly in phase.
ConstructiveDestructive You are 6? away from speaker A; 5? away from speaker B and at the speakers the waves are exactly out of phase.

Explanation / Answer

Firstly understand that PATH DIFFERENCE means length of the path of one wave MINUS length of path of other wave.

If the waves start off in phase, they will arrive in phase at a point if the PATH DIFFERENCE is zero, one wavelength, 2 wavelengths.... etc (ie whole number of wavelengths.) This gives CONSTRUCTIVE INTERFERENCE. If the PATH DIFFERENCE is an odd number of half wavelengths........they will arrive EXACTLY out of phase and will cancel out (DESTRUCTIVE INTERFERENCE).

Should the 2 waves set off in anti-phase(exactly out of phase), then a path difference of a whole number of wavelengths will mean they arrive still exactly out of phase (destructive interference)

Constructive interference (loud) when in phase (3 & 2.5).
Destructive interference (quiet) when out of phase (4 & 5).
When the sound waves meet somewhere (interfere) they add together (constructive) when in phase, or cancel out (destructive) when out of phase

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