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Doppler Effect and Sound (10 Points)?
A siren has a frequency of 718 Hz when it is at rest, whereas it has an apparent frequency of 876 Hz when it is moving toward a stationary observer. What is the speed of the siren in the latter case?
The answer is 61.9 m/s
I need help with the how-to, thank you.
1 Answer
- 8 years agoFavorite Answer
Hey,
The expression to be used here is,
f'=f(v+vo)/(v-vs), since the source and the listener are moving towards each other.
Here, f' is the apparent frequency, 876 Hz
f is the original frequency, 718 Hz
v = speed of the wave, in this case sound, so 340 m/s,
vo = speed of the observer, 0 m/s
vs = speed of the source, to be calculated.
876 = 718 * (340-0)/(340+vs)
=> 1.22 = 340/(340 + vs)
=> 414.8 + 1.22*vs = 340
=> 1.22*vs = -74.8
=> vs = -74.8/1.22
=> vs = -61.31 m/s
The difference caused is because of rounding errors. The speed is -ve, since the source is moving closer to the listener.
Hope this helped.
