Question

A siren emitting a sound of frequency $800Hz$ moves away from an observer towards a cliff at a speed of $15{ms}^{-1}$. Then, the frequency of sound that the observer hears in the echo reflected from the cliff is
(Take velocity of sound in air $=330{ms}^{-1}$)

• A. $765Hz$
• B. $800Hz$
• C. $838Hz$
• D. $885Hz$

Answer 1

The correct option is C $838Hz$

The general formula for apparent frequency is $f^{\prime }=\frac{v\pm u_O}{v\mp u_S}f$

As observer is at rest so $u_O=0$

Since the source moves towards cliff, i.e., effectively the source moves towards the observer (the sound being heard through echo), so $u_S$ taken as $-u_S=15m/s$

Thus, $f^{\prime }=\frac{v}{v-u_S}f=\frac{330}{330-15}800=838Hz$