Travelling along the Y-axis with a speed of 22 m s ⁻¹ , a source emits sound at a frequency of 4000 Hz . A listener is located on the ground at the coordinates (660 m , 0) . Determine the frequency of the sound detected by the listener at the exact moment the source crosses the origin. The speed of sound in air is 330 m s ⁻¹ .

Step-by-step solution

Let the source cross the origin at t = 0 . The sound detected by the listener at t = 0 was emitted by the source at an earlier time t = -t₀ . During the time interval t₀ , the sound travels a distance d = v t₀ , where v is the speed of sound. At t = -t₀ , the source was at a distance y = v_s t₀ from the origin along the Y-axis. The distance from the source at the time of emission to the listener at (660, 0) is d = 660^2 + y^2 . Thus, we have d = v t₀ . The component of the source's velocity along the line of sight