Question

A whistle of frequency 1000 Hz is sounded on a car travelling towards a cliff with velocity of $18m{s}^{-1}$ normal to the cliff. If $c=330m{s}^{-1}$, then the apparent frequency of the echo as heard by the car driver is nearly

• A. 1115 Hz
• B. 115 Hz
• C. 67 Hz
• D. 47.2 Hz

Answer 1

Answer: (A)

1115 Hz

The relationship between observed frequency (${\nu }^{\prime }$) and emitted

frequency (${\nu }_0$) is given by

${\nu }^{\prime }=\frac{v+u_r}{v+u_s}{\nu }_0$,

where v is the velocity of waves in the medium.

$u_r$ is the velocity of the receiver relative to the medium; positive if the receiver is moving towards the source (and negative in the other direction);

$u_s$ is the velocity of the source relative to the medium; positive if the source is moving away from the receiver (and negative in the other direction).

By the concept of acoustic, the observer and source are moving towards each other, each with a velocity of 18 m/s. So $u_r=18$ and $u_s=-18$ m/s

${\nu }^{\prime }=\frac{330+18}{330-18}1000=1115$ Hz.