Three sources of sound are distributed along a line, as shown in the figure, v i
ID: 1551071 • Letter: T
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 430 Hr. Source B is traveling at v/5 to the right, and it emits sound waves with a frequency of 1020 Hz. Source C is traveling at a speed of v/3 to the left, and it emits sound waves with a frequency of 1500 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 does A observe for the waves emitted by B? (A = observer; B = source) Hz What frequency does C observe for the waves emitted by A? (C = observer; A = source) Hz What frequency does B observe for the waves emitted by C? (B = observer; C = source) Hz 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?Explanation / Answer
Given
sources A B C
frequency 480 Hz 1020 Hz 1500 Hz
velocity rest v/5 v/3
v = 343 m/s
from Doppler's effect the apparent frequency is f' = f((v+/- v0)/(v+/-vs))
a) As B is moving away from A so A can observe less than 1020 Hz frequency of B
f' = fB(v-v0/v+vs)
f' = 1020 ((343-0)/(343+(343/5))) Hz
f' = 850 Hz
b) C is approaching A
f' = fA(v+v0 / v-vs)
f' = 480((343+(343/3))/(343-0)) Hz
f' = 640 Hz
c)
here B,C are approaching each other
f' = fC(v+v0 / v-vs)
f' = 1500((343+(343/5))/(343-(343/3))) Hz
f' = 2700 Hz
d)
f'B = 2*fC = 2*1500 = 3000 Hz
then VB =?
3000 = 1500 (v+v0 / v-vs)
3000 = 1500((343+v0)/(343-(343/3))) Hz
v0 = 3*v
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