Question

A speeding motorcyclist sees traffic jam ahead of him. He slows down to 36 km/hour. He finds that traffic has eased and a car moving ahead of him at 18 km/hour is honking at a frequency of 1392 Hz. If the speed of sound is 343 m/s, the frequency of the honk as heard by him will be

• A. 1332 Hz
• B. 1372 Hz
• C. 1412 Hz
• D. 1454 Hz

Answer 1

Answer: (C)

1412 Hz

From the Doppler effect the apparent frequency of the sound when both observer and source is moving in the same direction is given by,

$f^{\prime }=f\left[\frac{v+v_o}{v+v_s}\right]$

where v = velocity of sound

$v_o$ = velocity of observer

$v_s$ velocity of source

$f^{\prime }=f\left[\frac{v+v_o}{v+v_s}\right]=1392\times \left(\frac{343+10}{343+5}\right)Hz$
$=[\frac{353}{348}\times (1392\left)\right]Hz=1412Hz$