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 3? away from speaker A; 2? away from speaker B and at the speakers the waves are exactly in 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 3? away from speaker A; 4? 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 out of phase.

Explanation / Answer

Condition for constructive interference is path difference is n*lamda ,where n = 1,2,3......

Condition for destructive interference is path difference is (n+0.5)*lamda ,where n = 1,2,3......

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

when they are in same phase

phase difference = (2*pi/lamda)*path difference

0 = (2*pi/lamda)*path difference

path difference = 0

so constructive interference takes place and loud noise

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

Now path difference is 0.5 lamda ,so destructive interference takes place and no voice

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You are 3? away from speaker A; 4? away from speaker B and at the speakers the waves are exactly out of phase.

when they are in out of phase

phase difference = (2*pi/lamda)*path difference

pi = (2*pi/lamda)*path difference

path difference = lamda/2

total path difference is lamda+ lamda/2 = 3*lamda/2

so destructive interference and no voice

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

path difference is lamda/2

so total path difference is lamda/2 + lamda/2 = lamda

so constructive interference takes place and loud noise

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