Question

An engine moving away from a vertical cliff blows a horn at frequency f. Its speed is 0.5% of the speed of sound in air. The frequency of the reflected sound received at the engine is :

• A. 0.990 f
• B. 0.995 f
• C. 1.005 f
• D. 1.010 f

Answer 1

The correct option is A 0.990 f

The frequency of the sound waves as received by the cliff is given using the Doppler shift formula as

$f_{cliff}=f\times \frac{c}{c+0.005c}=\frac{1}{1.005}f$

Thus, the frequency of the reflected sound wave from the cliff is $f_r=\frac{1}{1.005}f$

The engine now experiences a Doppler effect, where the frequency shift is given by

$f_e=f_r\times \frac{c-0.005c}{c}=f_r\times 0.995=\frac{0.995}{1.005}f\approx 0.990f$