A sinusoidal wave in a rope is described by the wave functio

A sinusoidal wave in a rope is described by the wave function y = 0.20 sin (0.73 pi x + 22 pi t) where x and y are in meters and t is in seconds. The rope has a linear mass density of 0.245 kg/m. The tension in the rope is provided by an arrangement like the one illustrated in the figure below. What is the mass of the suspended object? kg

Solution

Here ,

let the mass of the suspended object is m

y = 0.20 * sin(0.73 * pi * x + 22pi * t)

linear mass , u = 0.245 Kg/m

as speed of wave = sqrt(T/u)

22pi/(0.73 * pi) = sqrt(M * 9.8/(0.245))

solving for M

M = 22.7 Kg

the hanging mass is 22.7 Kg