Two small speakers A and B are driven in step at 730 Hz by the same audio oscill

Question

Two small speakers A and B are driven in step at 730 Hz by the same audio oscillator. These speakers both start out 4.50 mfrom the listener, but speaker A is slowly moved away. (See the figure (Figure 1) ). The speed of sound in air is 344 m/s .

A. At what distance d will the sound from the speakers first produce destructive interference at the location of the listener?

B. If A keeps moving, at what distance d will the speakers next produce destructive interference at the listener?

C. After A starts moving away, at what distance will the speakers first produce constructive interference at the listener?

Explanation / Answer

A.
Let us find the wavelength 1st
use:
v= f*lambda
344 = 730* lambda
lambda = 0.47 m

first destructive interference occurs when path difference is lambda/2
path difference = d
d = lambda/2
d = 0.47/2
= 0.235 m

B.
2nd destructive interference occurs when path difference is 3*lambda/2
path difference = d
d =3* lambda/2
d = 3* 0.47/2
= 0.705 m

C.
first constructive interference occurs when path difference is lambda
path difference = d
d = lambda
d = 0.47 m

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