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 = 140 m .

Step-by-step solution

The position of the sound source is at the origin (0, 0) . The position of the listener is (336, 140) . The distance between the source and the listener is: r = 336^2 + 140^2 = 112896 + 19600 = 132496 = 364 m Assuming the listener travels in the positive y-direction, the velocity of the listener is v _L = 26 j m s ⁻¹ . The unit vector along the line joining the source to the listener is: r = 336 i + 140 j 364 = 12 13 i + 5 13 j The component of the listener's velocity along the line of sight (away from the source)