A police car moving at $22 m/s$, chases a motorcyclist. The police man sounds his horn at $176 Hz$, while both of them move towards a stationary siren of frequency $165 Hz$. Calculate the speed of the motorcycle, if it is given that he does not observes any beats .... $m/s$
IIT 2003, Diffcult
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(b) ${n_1}$ = Frequency of the police car horn observer heard by motorcyclist
${n_2}$ = Frequency of the siren heard by motorcyclist.
$v_2$ = Speed of motor cyclist
${n_1}$ = $\frac{{330 - v}}{{330 - 22}} \times 176\,\,;\,\,{n_2} = \frac{{330 + v}}{{330}} \times 165$
$\because {n_1} - {n_2} = 0 \Rightarrow v = 22 m/s$.
${n_2}$ = Frequency of the siren heard by motorcyclist.
$v_2$ = Speed of motor cyclist
${n_1}$ = $\frac{{330 - v}}{{330 - 22}} \times 176\,\,;\,\,{n_2} = \frac{{330 + v}}{{330}} \times 165$
$\because {n_1} - {n_2} = 0 \Rightarrow v = 22 m/s$.
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