# Need help solving Doppler Effect with sound question

1. Mar 29, 2015

### GravityInTheX

1. The problem statement, all variables and given/known data
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

2. Relevant equations
f0=fs(1/(1+vs/v))

3. 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!

2. Mar 29, 2015

### Staff: Mentor

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. Mar 29, 2015

### GravityInTheX

So which equation would I use?

4. Mar 29, 2015

### Staff: Mentor

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. Mar 29, 2015

### hopelessphysics

how do you apply it relative to the air?

6. Mar 29, 2015

### GravityInTheX

Okay so I did this, and got 22 m/s. Is this correct?

Sorry for the messy handwriting

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7. Mar 29, 2015

### hopelessphysics

isn't the original equation fo=fs(1+- vo/v)/(1+-vs/v)

8. Mar 29, 2015

### Staff: Mentor

That's both steps (ambulance and our car) combined, yes.

22m/s is correct.

9. Mar 29, 2015

### GravityInTheX

Thank you so much!