JEE Main · 2009 · 12 Apr 2009 · Offline · Waves & Sound

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 sire. 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}

(A)49 m
(B)98 m✓ Correct
(C)147 m
(D)196 m

Answer: (B)

Solution

The rider is the moving observer and the siren is the stationary source, so the heard frequency is

f^{'} = f \frac{v - v _{O}}{v}

. Setting

f^{'} = 0.94 f

with

v = 330 m/s

gives

v_{O} = 0.06 \times 330 = 19.8 m/s

. Starting from rest with

a = 2 m/ s^{2}

, the distance covered when this speed is reached is

s = \frac{v _{O}^{2}}{2 a} = \frac{19. 8 ^{2}}{4}

, which is about 98 m.

JEE Main · 2009 · 12 Apr 2009 · Offline · Single correct option

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