Q. A racing car moving towards a cliff sounds its horn. The drivers observe that the sound reflected from the cliff has a pitch one octave higher than the actual sound of the horn. If v=the velocity of sound, the velocity of the car is
A) $v/\sqrt{2}$
B) $v/2$
C) $v/3$
D) $v/4$
Explanation
(c) Let $n$ be the actual frequency of sound of horn.
If $v_{s}$ is velocity of car, then frequency of sound striking the cliff (source moving towards listener)
$n^{'} = \frac{\left( v + v_{s} \right)n^{'}}{v} = \frac{\left( v + v_{s} \right)}{v} \times \frac{v \times n}{\left( v - v_{s} \right)}$
Or $\frac{n^{''}}{n} = \frac{v + v_{s}}{v - v_{s}} = 2$
$v + v_{s} = 2v - 2v_{s}$
$3v_{s} = v,\ v_{s} = \frac{v}{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.