Question

A truck moving at a speed of 144km/hr passes a car moving at a speed of 72 km/hr .. If the truck sounds its horn at a frequency of 500Hz , what is the frequency of sound heard by the person the car?

Answer 1

Answer on Question #66375 – Mechanics – Relativity

A truck moving at a speed of $v = 144\frac{\mathrm{km}}{\mathrm{hr}} = 40\frac{\mathrm{m}}{\mathrm{s}}$ passes a car moving at a speed of $u = 72\frac{\mathrm{km}}{\mathrm{hr}} = 20\mathrm{m/s}$. If the truck sounds its horn at a frequency of $f_0 = 500\mathrm{Hz}$, what is the frequency of sound heard by the person the car?

Solution

The change of frequency (the Doppler shift) is

$$\Delta f = \frac {v - u}{c} f _ {0}.$$

Here $c = 343\frac{\mathrm{m}}{\mathrm{s}}$ is the speed of a sound in air.

So

$$\Delta f = \frac {40 - 20}{343}500 \approx 29\mathrm{Hz}.$$

Finally, the frequency of sound heard by the person the car is

$$f = \Delta f + f _ {0} = 29 + 500 = 529\mathrm{Hz}.$$

Answers: 529 Hz.

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