Question

The linear density of a string is 1.5 x 10^-4 kg/m. A transverse wave on the string is described by the equation y = (0.036 m) sin[(1.6 m^-1)x + (23 s^-1)t] What are the wave speed and the tension in the string?

Answer 1

The wave equation for a transverse wave is
y(x,t) = ym sin ( kx - $\omega$ t )
Where y(x,t) is the displacement of an element of the wave
Wave speed v = $\omega$ / k
Where $\omega$ is the angular frequency
f = 23 s^-1 , $\omega$   = 23 rad /s
k = 1.6 m^-1
v = 23 / 1.6 = 14.375 m / s
The tension in the string
T = v² $\mu$
Where T is the tension in the string and $\mu$ is the linear density of the string
T = (14.375)² x 1.5 x 10^-4
T = 0.030996 kg m /s²
or
T = 0.0310 N