The displacement of a string carrying a travelling wave is given by y = 3 ( ( 0.5 x - 50 t ) ) , where x and y are in centimetres and t is in seconds. What is the ratio of the maximum particle velocity to the wave velocity?

Step-by-step solution

Comparing the given equation y = 3 (0.5 x - 50 t) with the standard wave equation y = A (kx - t) , we get: Amplitude, A = 3 cm Angular wave number, k = 0.5 cm ⁻¹ Angular frequency, = 50 rad/s Maximum particle velocity is given by: v_ p,max = A = 3 50 = 150 cm/s Wave velocity is given by: v_w = k = 50 0.5 = 100 cm/s The ratio of maximum particle velocity to wave velocity is: v_ p,max v_w = 150 100 = 3 2 Answer: 3 2