Physics Question - speed of a wave?

Question

Just one tricky problem I can't seem to figure out:

A transverse wave is traveling on a string. The displacement y of a particle from its equilibrium position is given by y = (0.021 m)sin(29t - 2x). Note that the phase angle (29t - 2.0x) is in radians, t is in seconds, and x is in meters. The linear density of the string is 1.4x10^-2 kg/m. What is the tension in the string?

Thanks for any help!

Answer 1

The speed of a travelling wave on a string is given by

v = √[T/µ], where T = tension and µ = density. Therefore

T = v^2*µ

The speed of a travelling wave is given by w/k, if the wave equation is in the form y = A*sin(w*t - k*x), In your example, w = 29sec^-1, k = 2m^-1, so v = 29/2 = 14.5 m/sec. Then

T = 14.5^2 / 1.4*10^-2 = 2.94 newton