A.) For what values of x1 and x2 will destructive interference occur at point P?

Question

A.) For what values of x1 and x2 will destructive interference occur at point P? B.) For what values of x1, x2, x3 will be constructive interference at point P? C.) Interference effects like those in A and B are almost never a factor in listening to home stereo equipment. Why not? Exercise 16.34 Two loudspeakers, A and B (the figure), are driven by the same amplifier and emit sinusoidal waves in phase. Speaker B is 2.00 m to the right of speaker A. The frequency of the sound waves produced by the loudspeakers is 206 Hz. Consider point P between the speakers and along the line connecting them, a distance x to the right of speaker A. Both speakersemit sound waves that travel directly from the speaker to point P 2.00 m- 2.00m1.00m +-100m

Explanation / Answer

f = 206 Hz
speed of sound = 343 m/s
lambda = speed/f
= 343/206
= 1.665 m

if P is in between , A and B,
path difefrence= 2-x-x = 2-2x
A)
for destructive interfernce,
path difference = (m+1/2)*lamda
for m = 0.
path difference = lambda/2
2-2x = 1.665/2
2-2x = 0.8325
x = 0.58 m
That is x 1 = 0.58 m

for m = 1
path difference = 3*lambda/2
2-2x = 3*1.665/2
2-2x = 2.4975
x = 0.25 m
That is x 2 = 0.25 m

B)
for constructive interference,
path difference = (m)*lamda
for m = 1
path difference = lambda
2-2x = 1.665
x = 0.17 m
this is x1 = 0.17 m

for m = 2
path difference = lambda
2-2x = 2*1.665
x = -0.7 m
this is x2 = -0.7 m

for m = 3
path difference = lambda
2-2x = 3*1.665
x = -1.5 m
this is x3 = 1.5 m

C)
It is not factor because sound is reflected continuously from wall
And there is no definite places where constructive or destructive intereference takes place.

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