Two train whistles, A and B, each have a frequency of 412 H z . A is stationary

Question

Two train whistles, A and B, each have a frequency of 412Hz . A is stationary and B is moving toward the right (away from A) at a speed of 35.0m/s . A listener is between the two whistles and is moving toward the right with a speed of 15.0m/s

A. What is the frequency from A as heard by the listener?

B. What is the frequency from B as heard by the listener?

C. What is the beat frequency detected by the listener?

Two train whistles, A and B, each have a frequency of 412Hz . A is stationary and B is moving toward the right (away from A) at a speed of 35.0m/s . A listener is between the two whistles and is moving toward the right with a speed of 15.0m/s What is the frequency from A as heard by the listener? What is the frequency from B as heard by the listener? What is the beat frequency detected by the listener?

Explanation / Answer

this is doppler effect.
observed frequency=f=((v+vl)/(v+vs))*fo
v=velocity of wave in medium=343m/s
vl=velocity of listener(+ if listener moving towards the source and - if moving away from source)
vs=velocity of source(+if source moving away from observer and - if source moving towards observer)
a)v=343,
vl= -15
vs=0
f0=412
fa =((343-15)/(343))*412 = 393.98 Hz

b)

v=343
vl=15
vs=35
f0=392
fb = ((343+15)/(343+35))*412 = 390.2 Hz

c)beat frequency=fa-fb = 3.779 Hz

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