Need help solving Doppler Effect with sound question

  • #1
GravityInTheX
4
0

Homework Statement


As you drive at a speed of 15.0 m/s an ambulance approaches you from behind with its siren blaring at a frequency of 1022 Hz. After the ambulance has passed you the signal is now 981 Hz. If both you and the ambulance travel at a constant speed how fast was the ambulance traveling?

A. 16.0 m/s
B. 18.0 m/s
C. 20.0 m/s
D. 22.0 m/s
E. 24.0 m/s

Homework Equations


f0=fs(1/(1+vs/v))

The Attempt at a Solution


I figured I could use the ambulance's speed relative to the car, so I used the above equation for when a source is moving away from a stationary observer. I plugged in all the variables an solved for vs. I ended up getting vs being equal to 14.33. I then assumed since the speed was calculated with the car having a speed of 0 m/s, I simply added the speed of the car. That got me 29.33 m/s, which doesn't happen to be an answer choice. What am I doing wrong? Thank you so much!
 
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  • #2
Doppler effect of sound does not depend on the relative velocities alone, you cannot find the relative velocity without taking into account that you move relative to the air.
 
  • #3
So which equation would I use?
 
  • #4
You can still use this equation, but you have to apply it first to the ambulance (relative to the air) and then to you (relative to their air).
 
  • #5
how do you apply it relative to the air?
 
  • #6
Okay so I did this, and got 22 m/s. Is this correct?

Sorry for the messy handwriting
 

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  • #7
isn't the original equation fo=fs(1+- vo/v)/(1+-vs/v)
 
  • #8
hopelessphysics said:
isn't the original equation fo=fs(1+- vo/v)/(1+-vs/v)
That's both steps (ambulance and our car) combined, yes.

22m/s is correct.
 
  • #9
Thank you so much!
 
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