A police car moving at \(22 \mathrm{~ms}^{-1}\) chases a motor cyclist. The police man sounds horn at \(176…

1. \(33 \mathrm{~ms}^{-1}\)
2. \(22 \mathrm{~ms}^{-1}\)
3. \(44 \mathrm{~ms}^{-1}\)
4. \(11 \mathrm{~ms}^{-1}\)

Solution

According to the question, we draw the following situation,
Given, velocity of car, \(v_{s_1}=22 \mathrm{~ms}^{-1}\) speed of the sound in air, \(v=330 \mathrm{~ms}^{-1}\) apparent frequency by cyclist from the police car, \(\begin{aligned} f_1^{\prime} & =\frac{v-v_0}{v-v_s} f_1 \Rightarrow f_1^{\prime}=\frac{330-v_0}{330-22} \times 176 \\ & =\frac{330-v_0}{308} \times 176 \end{aligned}\) apparent frequency by cyclist from the stationary siren, \(f_2^{\prime}=\frac{v+v_0}{v} f_2=\frac{330+v_0}{330} \times 165\) Number of beats heard by the cyclist, \(\begin{aligned} & n=f_1^{\prime}-f_2^{\prime}=0 \text { (Given, } n=0 \text { ) } \\ & f_1^{\prime}=f_2^{\prime} \\ & \Rightarrow \quad\left(330-v_0\right) \frac{176}{308}=\left(330+v_0\right) \frac{165}{330} \\ & \Rightarrow \quad v_0=22 \mathrm{~ms}^{-1} \end{aligned}\) \(\therefore\) Hence, the speed of motorcycle is \(22 \mathrm{~ms}^{-1}\). So, the correct option is (b).

Asked in: AP EAMCET 2019 (23 Apr Shift 1)

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