Question

A motor cycle starts from rest and accelerates along a straight path at $2m/s^2$. At the starting point of the motor cycle there is a stationary electric siren. How far has the motor cycle gone when the driver hears the frequency of the siren at $94\%$ of its value when the motor cycle was at rest?(Speed of sound $=330m{s}^{-1}$)

• A. $147$m
• B. $196$m
• C. $225$m
• D. $98$m

Answer 1

Answer: (C)

$225$m

Doppler's effect of frequency of source of sound when source is stationary and the observer is moving away from source of sound is given by:

${\nu }^{\prime }=\nu \times \frac{(v-v_o)}{v}$

We are given${\nu }^{\prime }=\frac{90}{100}\nu$

$v=300\frac{m}{s}$ and

$v_0=2\sqrt{s}$

Therefore$\frac{90}{100}\nu =\nu \times \frac{(300-2\sqrt{s})}{300}$

or $270=300-2\sqrt{s}$

or $2\sqrt{s}=30$

or $s=225m$