Question

b) A harmonic wave on a rope is described by y(x,) (4.0 mm)siOx)] 2π 0.82 m i) Calculate the wavelength and time period of the wave. ii) Determine the displacement and acceleration of the element of the rope located at x = 0.58 m at time, t = 0.41 s. (4+6)

Please mention the name of the symbols that will be used later on the solution

Answer 1

y(x, t) = (4.0 mm) sin (2 pi/0.82 ((10 ms^-1) t + x)] comparing with y = A sin [k (vt + x)] (i) k = 2 pi/0.82 wave length lambda = 2 pi/k lambda = 2 pi/2 pi times 0.82 lambda = 0.82 m Time period T = 2 pi/omega T = 2 pi/kv T = 2 pi/2 pi/0.82 times 10 T = 0.082 sec (ii) at x = 0.58 m at t = 0.41 sec displacement y = (4 mm)S_m [2 pi/0.82 (10 times 0.41 + 0.58)] y = -3.9 mm acceleration a = -omega^2 y a = -4 pi^2/T^2 y a = -4 pi^2/(0.82)^2 times -3.9 times 10^-3 a = 22.9 m/s^2