A bullet travels past a person at a speed of 220 m/s . Determine the fractional change in the frequency of the whistling sound perceived by the person as the bullet crosses them. Take the speed of sound in air to be 330 m/s .

Step-by-step solution

Let the actual frequency of the whistling sound be f₀ . When the bullet approaches the stationary person, the apparent frequency f₁ is given by the Doppler effect formula: f₁ = f₀ ( v v - v_s ) Substituting v = 330 m/s and v_s = 220 m/s : f₁ = f₀ ( 330 330 - 220 ) = f₀ ( 330 110 ) = 3f₀ When the bullet recedes from the person, the apparent frequency f₂ is: f₂ = f₀ ( v v + v_s ) f₂ = f₀ ( 330 330 + 220 ) = f₀ ( 330 550 ) = 0.6f₀ The change in the perceived frequency as the bullet crosses the person is: f = f₁ - f₂ =