A police car moving at 22 ,ms^{-1} chases a m | vedclass

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Question

(B) Given: Velocity of the police car, $v_{s_1} = 22 \,ms^{-1}$.Speed of sound in air, $v = 330 \,ms^{-1}$.Frequency of the police car horn, $f_1 = 17

Vedclass · Accepted Answer

$22$

Vedclass · Answer

(B) Given: Velocity of the police car, $v_{s_1} = 22 \,ms^{-1}$.Speed of sound in air, $v = 330 \,ms^{-1}$.Frequency of the police car horn, $f_1 = 176 \,Hz$.Frequency of the stationary siren, $f_2 = 165 \,Hz$.Let the velocity of the motorcyclist be $v_0$.The apparent frequency $f_1^{\prime}$ heard by the motorcyclist from the police car (source moving towards observer, observer moving away from source) is:$f_1^{\prime} = \left( \frac{v - v_0}{v - v_{s_1}} ight) f_1 = \left( \frac{330 - v_0}{330 - 22} ight) 	imes 176 = \left( \frac{330 - v_0}{308} ight) 	imes 176$The apparent frequency $f_2^{\prime}$ heard by the motorcyclist from the stationary siren (source stationary, observer moving towards source) is:$f_2^{\prime} = \left( \frac{v + v_0}{v} ight) f_2 = \left( \frac{330 + v_0}{330} ight) 	imes 165$Since the number of beats heard is zero, $f_1^{\prime} = f_2^{\prime}$:$\left( \frac{330 - v_0}{308} ight) 	imes 176 = \left( \frac{330 + v_0}{330} ight) 	imes 165$$\left( 330 - v_0 ight) 	imes \frac{176}{308} = \left( 330 + v_0 ight) 	imes \frac{165}{330}$$\left( 330 - v_0 ight) 	imes 0.5714 = \left( 330 + v_0 ight) 	imes 0.5$$188.56 - 0.5714 v_0 = 165 + 0.5 v_0$$23.56 = 1.0714 v_0$$v_0 = 22 \,ms^{-1}$Thus, the speed of the motorcycle is $22 \,ms^{-1}$. The correct option is $(b)$.

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