Question

A train is moving in an elliptical orbit in anticlockwise sense with a speed of 110 m/s. Guard is also moving in the given direction with same speed as that of train. The ratio of the length of major and minor axes is $\frac{4}{3}.$ Driver blows a whistle of 1900 Hz at P, which is received by guard at S. The frequency received by guard is (velocity of sound v = 330 m/s)

• A. 1900 Hz
• B. 1800 Hz
• C. 2000 Hz
• D. 1500 Hz

Answer 1

The correct option is B 1800 Hz

Frequency received by guard is

$n_0=n_0\frac{v_0(v+v_{0}cos{\theta }_1)}{(v+v_{s}cos{\theta }_2)}$
v = 330 m/s
Here, $v_0=v_S=\frac{v}{3},cos{\theta }_1=\frac{3}{5},cos{\theta }_2=\frac{4}{5}$
$\therefore n=n_0\frac{(v+\frac{v}{3}\times \frac{3}{5})}{(v+\frac{v}{3}\times \frac{4}{5})}$
$=(\frac{6}{5}\times \frac{15}{19})n_0=\frac{18n_0}{19}=1800Hz$