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Doppler Effect Question regarding wavelength changing

1. Homework Statement

A listener L hears the siren from a moving police car ,S, which is moving away from the listener with a speed of v = 20.0 m/s. The listener is moving at 10.0 m/s towards the car. There is a wind blowing with a speed of v(wind)= 10.0 m/s from S to L. The siren is emitting sound at a frequency (f) of 800 Hz. The velocity of sound in air is 343 m/s. Calculate the frequency (f') heard by the listener and the wavelength (λ) of that wave.



2. Homework Equations

f' = f(v +/- vD) / (v -/+ vS)
v = fλ

3. The Attempt at a Solution

Finding the new frequency is easy:

f' = (800hz)(343+10+ 10)/(343+10+20)
f' = 779 Hz.


But now for finding the wavelength I'm confused.
I know it's λ = v/f'

but is it:
v = 343m/s (the speed of sound in still air)
v= 343+10 m/s (the speed of sound + the speed of the wind)
v= 343+10+20 m/s (the speed of sound + the speed of the wind + the speed of the source)
or something else?

Any help would be much appreciated.
 
Last edited:

Simon Bridge

Science Advisor
Homework Helper
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The wavelength heard by the listener is the frequency of the sound divided by the speed the wave is passing the listener.
 
The wavelength heard by the listener is the frequency of the sound divided by the speed the wave is passing the listener.
My apologies, I put the wrong question (I had v = f/λ when it should be v= fλ); I fixed this up now.

But by your statement would be the last option I suggested? λ = (speed of sound + speed of wind + speed of source)/(new frequency)?
 

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