Question

Two trains move towards each other with the same speed. The speed of sound is $340m/s$. If the height of the tone of the whistle of one of them heard on the other changes to $9/8$ 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

Answer 1

Answer: (A)

According to Doppler effect the the pitch of a sound change due the motion of source is given by:
$\overline{n}=n\frac{v-v_0}{v-v_s}$
Here, $v_s$ and $v_0$ are the velocity of the sound source and observer and $v=330m/s$ and $\overline{n}/n=9/8$.
Lets assume the velocity of both the the trains are $\bar{v}$.
Using the above formula:
$\overline{n}/n=9/8=\frac{v-(-\overline{v})}{v-\overline{v}}$.
The negative sign used for the opposite direction movement of the trains.
Using all the known values we can get the velocity of the trains are $20m/s$.