A boy riding on his bike is travelling towards the east at a speed of 4 2 m s ⁻¹ . At a particular instant, he generates a sound pulse with a frequency of 1650 Hz which travels through the air at a speed of 334 m s ⁻¹ . Another boy is standing on the ground 45^ south of east relative to him. Determine the frequency of the pulse as received by the second boy.

Step-by-step solution

The velocity of the source is v_s = 4 2 m s ⁻¹ towards the east. The observer is stationary, so v_o = 0 . The position of the observer relative to the source is 45^ south of east. The component of the source's velocity along the line joining the source and the observer is: v_ s, eff = v_s (45^ ) = 4 2 1 2 = 4 m s ⁻¹ Using the Doppler effect formula for a stationary observer and a moving source, the apparent frequency f' is given by: f' = f₀ ( v v - v_ s, eff ) Substituting the given values f₀ = 1650 Hz and v = 334