Question

A cord is stretched with tension 102 N between two supports 28.4 m apart. If it takes a pulse 0.430 s to travel from one support to the other, what is the mass of the string?

Answer 1

On a string the wave propagates with velocity

$v=\lambda\nu=\frac{\lambda}{T}=66m/s$

where the wavelength is the chord length. This propagation velocity depends upon the string tension and linear mass density.

$v=\sqrt{\frac{T}{\mu}}$

And the linear mass density is

$\mu=\frac{T}{v^2}=0.023 kg/m$

The corresponding mass is

$m=\mu L=0.66 kg$