How Fast is the Racecar Moving Based on the Doppler Effect?

[BlueSkyy]

Homework Statement

The pitch of the sound from a racecar engine drops the musical interval of a fourth when it passes the spectators. This means the frequency of the sound after passing is 0.75 times what it was before. How fast is the racecar moving?
1. 61 m/s
2. 49 m/s
3. 72 m/s
4. 68 m/s

Homework Equations

fo = fs / 1 - (vs/v)

The Attempt at a Solution

I tried using 75 = 100 / (1 - (vs/331) to solve for the speed of the source, but my answer was way off...there's got to be something I'm missing. am i correct in thinking i need to use v = 331 for the speed of sound? then what do i use for fo and fs?

 

[G01]

Your problem is that fs is not 100.

100 is the observed frequency for when the car is moving toward you.

Then 75, would be the observed frequency for when the car is moving away from you.

So you are going to have to set up two doppler shift equations, one for when the car is moving toward and the other for when the car is moving away from you.

So, after you have these two equations, how would you solve for v?