Question

Two trains move towards each other with the same speed. The speed of sound is 340 m/sec. 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. 2000 m/sec
• B. 200 m/sec
• C. 20 m/sec
• D. 2 m/sec

Answer 1

The correct option is C 20 m/sec

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 $\overline{v}$. 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.