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A motor cycle starts from rest and accelerates along a straight path at 2 m/s². At the starting point of the motor cycle there is a stationary electric siren. How far (in meter) 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)

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answer is 98.

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Detailed Solution

when source is stationary and observer is moving away from the source

$f' = (\frac{v - v_{0}}{v}) f$

$given f' = \frac{94 f}{100}$

$\frac{94 f}{100} = (\frac{330 - v_{0}}{330}) f$

$v_{0} = 330 (1 - \frac{94}{100}) = 19.8 m / s$

by this time displacement is

$s = \frac{v^{2}}{2 a} = \frac{{(19.8)}^{2}}{4} = 98.01 m \approx 98 m$

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