Question 139: Waves

Question

A car P travelling at $$20 \mathrm{~ms}^{-1}$$ sounds its horn at a frequency of $$400 \mathrm{~Hz}$$. Another car $$\mathrm{Q}$$ is travelling behind the first car in the same direction with a velocity $$40 \mathrm{~ms}^{-1}$$.

The frequency heard by the passenger of the car $$\mathrm{Q}$$ is approximately [Take, velocity of sound $$=360 \mathrm{~ms}^{-1}$$ ]

Accepted Answer

Using the Doppler effect formula:
$$f = f_0\left(\frac{c + v_0}{c + v_s}\right)$$
where
$$f$$ is the observed frequency (frequency heard by the passenger in car Q)
$$f_0$$ is the source frequency (400 Hz)
$$c$$ is the speed of sound (360 m/s)
$$v_0$$ is the velocity of the observer (passenger in car Q) relative to the medium (air) in the direction of the source (40 m/s)
$$v_s$$ is the velocity of the source (car P) relative to the medium (air) in the direction of the observer (20 m/s, since it's moving in the same direction as car Q)
Plugging in the values:
$$f = 400\left(\frac{360 + 40}{360 + 20}\right)$$
$$f = 400\left(\frac{400}{380}\right)$$
$$f = 421$$
So, the observed frequency is 421 Hz.

Answer

485 Hz

Answer

514 Hz

Answer

421 Hz

Answer

471 Hz

Waves

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