In: Physics
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.
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