A source of sound with natural frequency F₀ moves uniformly along a line separated from a stationary listener by a distance =42 5 ~m . The velocity of source is equal to n =0.5 fraction of velocity of sound. If the distance between source and listener at the moment when the listener receives actual frequency of the source is (21 n) meter, find the value of n .

Step-by-step solution

Let, V₀ velocity of sound when source is O at the velocity component of source towards listener is V_ s 90=0 F^ =F₀ ( V₀ V₀-V_S 90 )=F_S time taken by sound to reach listener = V ₀ . Distance moved by source in this time = ( V₀ ) V _ S Distance between source and listener = ^2+ n ^2 ^2 = 1+ n ^2 =105 ~m . 2. If the plank is displaced slightly by x towards left, then