Need help solving Doppler Effect with sound question

[GravityInTheX]

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=f_s(1/(1+v_s/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 v_s. I ended up getting v_s 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!

 

[mfb]

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.

 

[GravityInTheX]

So which equation would I use?

 

[mfb]

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).

 

[hopelessphysics]

how do you apply it relative to the air?

 

[GravityInTheX]

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

Sorry for the messy handwriting

 

[hopelessphysics]

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

 

[mfb]

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.

 

[GravityInTheX]

Thank you so much!