A train moves towards a stationary observer with speed $34 m/s$. The train sounds a whistle and its frequency registered by the observer is ${f_1}$. If the train’s speed is reduced to $17\, m/s$, the frequency registered is ${f_2}$. If the speed of sound is 340 m/s then the ratio ${f_1}/{f_2}$ is
IIT 2000, Medium
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(d) By using $n' = n\,\,\left( {\frac{v}{{v - {v_S}}}} \right)$
==>${f_1} = n\,\left( {\frac{v}{{v - {v_S}}}} \right)$
$ = n\,\left( {\frac{{340}}{{340 - 34}}} \right) = \frac{{340}}{{306}}n$
and ${f_2} = n\,\left( {\frac{{340}}{{340 - 17}}} \right) = n\,\left( {\frac{{340}}{{323}}} \right)$
$ \Rightarrow $$\frac{{{f_1}}}{{{f_2}}} = \frac{{323}}{{306}} = \frac{{19}}{{18}}$
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