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**[SOLVED] Doppler Shift and Beats**

**1. Homework Statement**

A car horn sounds a pure tone as the car approaches a wall. A stationary listener behind the car hears an average frequency of 250Hz, which pulsates (beats) at 12 Hz. What is the speed of the car?

The speed of sound is assumed to be 331 m/s

**2. Homework Equations**

f_beat = f1 - f2

f[tex]_{'}[/tex]=f [1 / (1+ VE/V)] Doppler Shift for Stationary Receiver, Receding Emitter.

**3. The Attempt at a Solution**

There must be two noises overlapping if the stationary listener is hearing a pulsating beat. If the average frequency heard is 250Hz, then (f1+f2) = 500. Plugging this into f_beat=f1-f2=12Hz, you find that the frequencies must be 244Hz and 256Hz. One of these frequencies is the result of the doppler shift as the listener receives the noise from the receding car. The other I assumed to be the noise that the listener received after it bounced off the wall (which the car is approaching). As far as I can tell, there must then be two equations in regards to the doppler shift for each sound, which share two common variables: f, the tone emitted by the car as if it wasn't moving, and VE, the speed of the car. One of these equations should be 244Hz = f[1 / (1 +VE/ 331m/s)], but I'm not sure how to go about calculating the other equation, or whether or not I'm on the right track in solving this.

Any help would be greatly appreciated.