Wave Motion 4 Question 13
6. 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 speed of the train is reduced to 17 $m / s$, the frequency registered is $f _2$. If speed of sound is 340 $m / s$, then the ratio $\frac{f _1}{f _2}$ is
(2019 Main, 10 Jan I)
(a) $\frac{19}{18}$
(b) $\frac{21}{20}$
(c) $\frac{20}{19}$
(d) $\frac{18}{17}$
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Solution:
- When a source is moving towards an stationary observer, observed frequency is given by
$$ f _{\text {observed }}=f\left(\frac{v}{v+v _s}\right) $$
where, $f=$ frequency of sound from the source, $v=$ speed of sound and $v _s=$ speed of source.
Now applying above formula to two different conditions given in problem, we get
$$ \begin{aligned} f _1 & =\text { Observed frequency }=f\left(\frac{340}{340-34}\right) \\ & =f\left(\frac{340}{306}\right) \end{aligned} $$
and $f _2=$ Observed frequency when speed of source is reduced
$$ =f\left(\frac{340}{340-17}\right)=\frac{340}{323} $$
So, the ratio $f _1: f _2$ is $\frac{f _1}{f _2}=\frac{323}{306}=\frac{19}{18}$.
