A man walks parallel to a railway track with a speed of 1.5 m/s, and a train moves towards him at a speed of 20 m/s. The man hears the train whistle with a frequency of 683 Hz. The speed of sound in air is equal to 340 m/s. What is the frequency of the whistle emitted by the train?


Problem data:

• Sound source velocity:    v_f = −20 m/s;
• Observer velocity:    v_o = 1.5 m/s;
• Frequency heard by the observer:    f_o = 683 Hz;
• Speed of sound in air:    v = 340 m/s.

Problem diagram:


We choose a reference frame pointing from the observer (man) to the sound source (train). We have the man with positive velocity, v_o > 0, and the train with a negative speed, v_f < 0 (Figure 1).

Solution

Due to the relative motion between the observer and the sound source, the frequency heard by man will be different from the frequency emitted by the train whistle, the Doppler Effect is given by