A train travelling at 108 km h^ -1 towards east whistles with a...

The passenger and the whistle are on the same train.

The relative velocity between the source of sound (whistle) and the observer (passenger) is zero.

According to the Doppler effect, the apparent frequency is given by f' = f \left(\dfrac{v - v_o}{v - v_s} \right).

Since both the source and the observer are moving with the same velocity in the same direction, $v_o = v_s$.

Substituting these values, we get $f' = f = 500 \text{ Hz}$.

The frequency heard by the passenger remains unchanged at $500 \text{ Hz}$.