Question

Two trains A and B are moving towards each other at a speed of 156.2m/s. If the frequency of the whistle emitted by A is 844.6Hz, then what is the apparent frequency of the whistle heard by the passenger sitting in train B. Note that the velocity of sound in air is 340m/s.

Answer 1

We can find the observed frequency of the whistle heard by the passenger sitting in train B from the Doppler Shift formula:

$$f_o=f_s(\dfrac{v+v_o}{v-v_s}),$$ $$f_o=844.6\ Hz\times(\dfrac{340\ \dfrac{m}{s}+156.2\ \dfrac{m}{s}}{340\ \dfrac{m}{s}-156.2\ \dfrac{m}{s}})=2280\ Hz.$$