Question

A racing car moving towards a cliff sounds its horn. The driver observes that the sound reflected from the cliff has a pitch one octave higher than the actual sound. lf V is the velocity of sound, what is the velocity of the car :

• A. $\frac{\vee }{\sqrt{2}}$
• B. $\frac{\vee }{2}$
• C. $\frac{\vee }{3}$
• D. $\frac{\vee }{4}$

Answer 1

The correct option is C $\frac{\vee }{3}$

let ${\nu }_c$ is the apparent freq at cliff and ${\nu }_s$ is the freq by the sound of the car, let $v_s$ is the velocity of the car and $V$ is the velocity of the sound in the air. Then from the Doppler effect,

${\nu }_c=\frac{V}{V-v_s}{\nu }_s$,

say the apparent freq of the reflected sound by the cliff is ${\nu }_c^{\prime }$, then

${\nu }_c^{\prime }=\frac{V+v_s}{V}{\nu }_c=\frac{V+v_s}{V-v_s}{\nu }_s$,

but we are given, ${\nu }_c^{\prime }=2{\nu }_s$

that will give us,

$\frac{V+v_s}{V-v_s}=2$,

by componendo-dividendo

$v_s=V/3$