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I've got this task:

A traffic policeman standing on the highway notices a change in tone of exactly one major third (f2/f1 = 4/5).

What speed can he infer? Speed of sound c = 340 m/s

I've got this attempt: 340 m/s * (1+√5/4) = 765m/S = 2754 km/h

Can someone tell me if this is correct or if I'm completely wrong?

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    $\begingroup$ Ahh -- homework? Has your book discussed how to derive the Doppler effect from first principles? Can you start with a car moving at 765m/s emitting a tone, and predict the tone perceived by a listener from those first principles? $\endgroup$
    – TimWescott
    Mar 17, 2021 at 2:33
  • $\begingroup$ Your proposed solution would require strapping a jet engine to the car. So, sorry, that's wrong. $\endgroup$
    – Hilmar
    Mar 17, 2021 at 2:50
  • $\begingroup$ Check here: en.wikipedia.org/wiki/Doppler_effect $\endgroup$
    – ZR Han
    Mar 17, 2021 at 6:47

1 Answer 1

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Hints

  1. Define the frequency of the car as $f_0$, the heard frequency when it's approaching as $f1$ and the heard frequency when it's departing as $f_2$
  2. Write the Doppler formula for both $f_1$ and $f_2$ using a receiver velocity of 0 (since the policeman is stationary with respect to the air) and a car velocity of $v_s$. Pay attention to the sign of the source velocity.
  3. Write the ratio of both formulas and equal it to a major third. $f_0$ should drop out and you are left with a single equation for $v_s$
  4. Solve for $v_s$
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