Question

A train is moving with a constant speed 15 m/s along a circular track. The length of the train makes an angle ${90}^{\circ }$ at the centre. A siren in its engine is emitting a sound of frequency 1.5kHz. The apparent frequency of sound as heard by a passenger at the rear end of the train is 100x Hz, then find x. (In Hz)

Answer 1

Velocity of source as well as that of observer ${\upsilon }_s=v_o=15m/s$
Original frequency $f=1.5kHz$
Apparent frequency heard $f^{{}^{\prime }}=100xHz$
Using Doppler effect when the source and observer are moving in same direction.
$f^{{}^{\prime }}=\left(\frac{\upsilon +{\upsilon }_0}{\upsilon -{\upsilon }_s}\right)\cdot f$
$\Rightarrow 100x=\left(\frac{340+15}{340-15}\right)\times 1.5\times {10}^3$
$\Rightarrow 100x=\frac{355}{325}\times 15\times 100$
$\Rightarrow x=15$