Wave Motion 5 Question 10
10. The spread of frequency as observed by the passengers in train $B$ is
(2007, 4M)
(a) $310 Hz$
(b) $330 Hz$
(c) $350 Hz$
(d) $290 Hz$
Passage 2
Two plane harmonic sound waves are expressed by the equations.
$$ \begin{aligned} & y _1(x, t)=A \cos (0.5 \pi x-100 \pi t) \\ & y _2(x, t)=A \cos (0.46 \pi x-92 \pi t) \end{aligned} $$
(All parameters are in MKS)
Show Answer
Solution:
- For the passengers in train $B$, observer is receding with velocity $30 m / s$ and source is approaching with velocity $20 m / s$.
$\therefore \quad f _1^{\prime}=800\left(\frac{340-30}{340-20}\right)=775 Hz$
and
$$ f _2^{\prime}=1120\left(\frac{340-30}{340-20}\right)=1085 Hz $$
$\therefore$ Spread of frequency $=f _2^{\prime}-f _1^{\prime}$
$$ =310 Hz $$
