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 of the horn. If $$v$$ is the velocity of sound then the velocity of the car is

A
v2
B
v2
C
v3
D
v4

Solution

## The correct option is B $$\displaystyle\frac{v}{3}$$Let velocity of car $$=v$$$$n^{'}=n\begin{bmatrix}\displaystyle\frac{v}{v-v_s}\end{bmatrix}\;\dots (i)\;\;\;\;\;n^{"}=n^{'}\begin{bmatrix}\displaystyle\frac{v+v_s}{v}\end{bmatrix}\;\dots (ii)$$From (i) & (ii) $$n^{"}=n\begin{bmatrix}\displaystyle\frac{v+v_{s}}{v-v_{s}}\end{bmatrix}$$Now $$\displaystyle\frac{n^{"}}{n}=2\Rightarrow \begin{pmatrix}\displaystyle\frac{v+v_s}{v-v_s}\end{pmatrix}=2$$$$\Rightarrow v+v_{s}=2v-2v_{s}\Rightarrow 3v_{s}=v\Rightarrow v_{s}=\displaystyle\frac{v}{3}$$Physics

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