Question

A train is moving with a constant speed $15m/s$ along a circular track. The length of the train makes an angle ${90}^0$ 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 $x/2kHz$, then find the value of $x$ :

Answer 1

When the Observer is approaching the Stationary source,
the apparent frequency, $f^{\prime }=\frac{v+v_O}{v+v_S}f$ where $v=$ velocity of sound.
here, $f^{\prime }=\frac{v+15\cos 45}{v+15\cos 45}f=f=1.5kHz=3/2kHz$
thus, $x=3$