Wave Motion 4 Question 24
23. An observer standing on a railway crossing receives frequency of $2.2 kHz$ and $1.8 kHz$ when the train approaches and recedes from the observer. Find the velocity of the train. (The speed of the sound in air is $300 m / s$.)
(2005, 2M)
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Answer:
Correct Answer: 23. $v_T=30 \mathrm{~m} / \mathrm{s}$
Solution:
- From the relation, $f^{\prime}=f\left(\frac{v}{v \pm v_s}\right)$, we have $$ \begin{aligned} & 2.2=f\left[\frac{300}{300-v_T}\right] \cdots(i)\\ and & 1.8=f\left[\frac{300}{300+v_T}\right] \cdots(ii)\\ \end{aligned} $$
Here, $v_T=v_s=$ velocity of source/train
Solving Eqs. (i) and (ii), we get $$ v_T=30 \mathrm{~m} / \mathrm{s} $$
