A car is moving towards a high cliff. The driver sounds a horn of...

A car is moving towards a high cliff. The driver sounds a horn of frequency

f

. The reflected sound herd by the driver has frequency

2 f

. If

v

is velocity of sound, then the velocity of the car, in the same velocity units, will be: A car is moving towards a high cliff. The driver sounds a horn of frequency f . The reflected sound herd by the driver

A car is moving towards a high cliff. The driver sounds a horn of frequency f . The reflected sound herd by the driver

Options

A $\frac{v}{\sqrt{2}}$
B $\frac{v}{3}$
C $\frac{v}{4}$
D $\frac{v}{2}$

Correct answer

B. $\frac{v}{3}$

Step-by-step solution

According to given condition A car is moving towards a high cliff. The driver sounds a horn of frequency f . The reflected sound herd by the driver

Cliff is stationary source of frequency

f

where f=

\left(\frac{V+V_{\text{car }}}{v}\right)

f^{\prime} Frequency heard by

the drives

\begin{array}{rlrl}f^{\prime \prime}=\left(\frac{V+V_{\mathrm{car}}}{v-v_{\mathrm{car}}}\right)f^1=\left(\frac{V+V_{\mathrm{car}}}{v-v_{\mathrm{car}}}\right)f \\ & =2 f \\ \Rightarrow & V+V_{\mathrm{car}} & =2 V-2 v_{\mathrm{car}} \\ \Rightarrow & 3 v_{\mathrm{car}} & =V \\ \Rightarrow & \quad V_{\mathrm{car}} & =\frac{v}{3} \end{array}

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