A sound source is fixed at the origin and continuously emits sound at a frequency of 660 Hz . The sound propagates through air at a speed of 330 m s ⁻¹ . A listener travels along the line x = 336 m with a constant speed of 26 m s ⁻¹ . Calculate the frequency of the sound observed by the listener when he is positioned at y = 0 .

Step-by-step solution

The sound source is stationary and fixed at the origin (0,0) . The listener travels along the line x = 336 m , which means the listener's velocity is directed along the y-axis (i.e., v _L = 26 j m s ⁻¹ ). When the listener is positioned at y = 0 , their coordinates are (336, 0) . The line of sight joining the source to the listener is along the x-axis. The angle between the listener's velocity vector (along the y-axis) and the line of sight (along the x-axis) is 90^ . The component of the listener's velocity along