# Speed of car with sound [closed]

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?

• 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? Mar 17, 2021 at 2:33
• Your proposed solution would require strapping a jet engine to the car. So, sorry, that's wrong. Mar 17, 2021 at 2:50
• Check here: en.wikipedia.org/wiki/Doppler_effect Mar 17, 2021 at 6:47

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 $$v_s$$