Three sources of sound are distributed along a line, as shown in the figure. v i

Question

Three sources of sound are distributed along a line, as shown in the figure. v is the speed of sound. Source A is at rest, and it emits sound waves with a frequency of 540 Hz. Source B is traveling at v/5 to the right, and it emits sound waves with a frequency of 1140 Hz. Source C is traveling at a speed of v/3 to the left, and it emits sound waves with a frequency of 1650 Hz. A, B, and C also detect the sound waves emitted by the other sources. All the questions below pertain to when the three sources of sound are at the locations shown in the figure below.

What frequency (in Hz) does B observe for the waves emitted by C? (B = observer; C = source)

To what value should B's speed be changed to so that B observes a frequency for the waves it receives from C that is exactly twice the frequency of the waves emitted by C? (v)

Explanation / Answer

the observer and source are approaching each other thefrequencyheard by the observer (f') is
f'=f(v+vo)/(v-vs)
If they are receding (moving away from each other)
f'=f(v-vo/v+vs)

v=speed of wave
vo=speed of observer
vs=speed of source
f=frequency at source
f'=frequency observed by observer.

(a) What frequency does A observe for the waves emitted by B? (A = observer; B = source)

= 1140* (v+0)/v = 1140Hz

(b) What frequency does C observe for the waves emitted by A? (C = observer; A = source)
Hz

= 540* (v-v/3)/(v-0) = 360Hz

(c) What frequency does B observe for the waves emitted by C? (B = observer; C = source)
Hz

=1650 [v/(v+v/3)] = 1237.5 Hz

d) let v' is the required velocity

1650 * (v+v')/(v+v/3) = 1.5 * 1400

this gives v+v' = 2v

thus v' = v

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