A motor cycle starts from rest and accelerates along a straight path at $2 \;m / s ^{2}$. 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 $=330 ms ^{-1}$)
AIEEE 2009, Diffcult
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Observer is in motion and source is at rest.
$\Rightarrow n^{\prime}=n \frac{v-v_{O}}{v+v S}$
$\Rightarrow \frac{94}{100} n=n \frac{330-v_{O}}{330}$
$\Rightarrow 330-v_{O}=\frac{330 \times 94}{100}$
$\Rightarrow v_{O}=330-\frac{94 \times 33}{10}=\frac{33 \times 6}{10} m / s$
$s=\frac{v^{2}-u^{2}}{2 a}=\frac{9 \times 33 \times 33}{100}=\frac{9 \times 1089}{100} \approx 98 m$
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