A white car is driving along one day and comes up behind a red car moving slower

Question

A white car is driving along one day and comes up behind a red car moving slower. the driver honks his horn at the red car. The horn has a frequency of 1200 Hz and the speed of sound on this day is 355 m/s. Just behind the red car is a green car heading in the other direction that just passed the red car. Also, there is a faster moving blue car approaching the red and white cars.
Red car--22 m/s; White car--33 m/s; Green Car-- 25 m/s; Blue Car--38 m/s
What frequency does each of the four drivers hear?

Explanation / Answer

The white car will perceive the frequency as given -- 1200Hz

To find the other perceived frequencies, you can use

f'=f[vo + vd/vo - vs] when the cars are approaching one another
f'=f[vo - vd/vo - vs] when the cars are moving away from one another

1) red car

Since the Doppler effect is concerned with relative velocities, you can consider the white car moving at a relative speed of 33-22=11m/s towards the red car. You will use the first equation:

f'=1200[347/(347 - 11)]=1239.28 Hz

2) green car

Use the first equation again:

f'=1200[(347+25)/(347-33)]=1421.65 Hz

3) blue car

f'=1200[(347+38)/(347-33)]=1471.33 Hz

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