A train approaching a railway crossing at a speed of 120 km/h sounds a short whistle at frequency 640 Hz when it is 300m away from the crossing. The speed of sound in air is 340 m/s. What will be the frequency heard by a person standing on a road perpendicular to the track through the crossing at a distance of 400m from the crossing.(in HZ)

The observer A is at rest with respect to the air and the source is travelling at a velocity of 120 km/h i.e., 100/3 m/s. As is clear from figure, the person receives the sound of the whistle in a direction BA making an angle $\mathrm{\theta }$ with the track where cos$\mathrm{\theta }$ = 300 / 500 = 3 / 5. The component of the velocity of the source (i.e., of the train.) 
along with this direction AB is $\frac{100}{3}\times \frac{3}{5}\mathrm{m}/\mathrm{s}=20\mathrm{m}/\mathrm{s}$.
As the source is approaching the person with this component, the frequency heard by the observer is.
$\mathrm{v}=\frac{\mathrm{v}}{\mathrm{v}-{\mathrm{v}}_{\mathrm{s}}\cos \mathrm{\theta }}\Rightarrow \mathrm{v}=\frac{340}{340-20}\times 640\mathrm{Hz}\Rightarrow 680\mathrm{Hz}$