Wave Motion 4 Question 12
12. A siren placed at a railway platform is emitting sound of frequency $5 \mathrm{kHz}$. A passenger sitting in a moving train $A$ records a frequency of $5.5 \mathrm{kHz}$, while the train approaches the siren. During his return journey in a different train $B$ he records a frequency of $6.0 \mathrm{kHz}$ while approaching the same siren. The ratio of the velocity of $\operatorname{train} B$ to that of $\operatorname{train} A$ is
$(2002,2 M)$
(a) $242 / 252$
(b) 2
(c) $5 / 6$
(d) $11 / 6$
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Answer:
Correct Answer: 12. (b)
Solution:
- Using the formula $f^{\prime}=f\left(\frac{v+v_0}{v}\right)$ we get, $$ 5.5=5\left(\frac{v+v_A}{v}\right) \cdots(i) $$ and $$ 6.0=5\left(\frac{v+v_B}{v}\right) \cdots(ii) $$
Here, $$ \begin{aligned} v & =\text { speed of sound } \ v_A & =\text { speed of train } A \ v_B & =\text { speed of train } B \end{aligned} $$
Solving Eqs. (i) and (ii), we get $\frac{v_B}{v_A}=2$
