Question

Two engines travelling in opposite directions at 72 km/hr. One engine sounds a whistle of frequency 1088 cps. If the speed of sound is 340 m/sec, then frequency heard by the observer on the other engine after crossing will be :

• A. 9640 Hz
• B. 964 Hz
• C. 96.4 Hz
• D. 9.64 Hz

Answer 1

Answer: (B)

964 Hz

According to Doppler effect the pitch of a sound change due the motion of source is given by:

$\overline{n}=n\frac{v-v_s}{v-v_0}$

Here, $v_s$ and $v_0$ are the velocity of the sound source and

observer and $v=330m/s$ is the velocity of sound in air . The velocity of both the trains are $\overline{v}=72km/hr=20m/s$.

Using the above formula,

$\overline{n}=n\frac{v-(-\overline{v})}{v-\overline{v}}$. The negative sign used for the

opposite direction movement of the trains.

$\overline{n}=n\frac{v-\overline{v}}{v-(-\overline{v})}=1088\times \left(\frac{330-20}{330+20}\right)=964Hz$