### Waves - Result Question 80

#### 82. Two trains move towards each other with the same speed. The speed of sound is $340 m / s$. If the height of the tone of the whistle of one of them heard on the other changes $9 / 8$ times, then the speed of each train should be

(a) $20 m / s$

(b) $2 m / s$

(c) $200 m / s$

(d) $2000 m / s$

[1991]

## Show Answer

#### Answer:

Correct Answer: 82. (a)

Solution:

- (a) Here, $v^{\prime}=\frac{9}{8} v$

Source and observer are moving in opposite direction, therefore, apparent frequency

$v^{\prime}=v \times \frac{(v+u)}{(v-u)}$

$\frac{9}{8} v=v \times(\frac{340+u}{340-u})$

$\Rightarrow 9 \times 340-9 u=8 \times 340+8 u$

$\Rightarrow 17 u=340 \times 1 \Rightarrow u=\frac{340}{17}=20 m / sec$.