# Two train whistles, A and B, each have a frequency of 392 Hz. 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. No wind is blowing. 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?

note:

(there are no question mark”?” in the right (away from A) is the continuations ty…)

• 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=392

fa can be found.

b)v=343

vl=15

vs=35

f0=392

fb can be found.

c)beat frequency=fa-fb

• with respect to A the listener is opening the distance at 15 m/s

F = Fo ( V / ( V + Vl )

where V is speed of sound and Vl is relative speed of listener

F = 392 ( 343 / (343+15) = 375.6

with respect to B the source is moving away from the listener at 20 m/s

F = Fo ( ( V – Vs ) / V

where Vs is the speed of the source

F = 392 ( (343-20) / 343 ) = 369.1

the difference gives 6.5 beats/sec

• B