Question

What is the maximum speed of a wave on a cable with length of 50 m, mass of 200 kg, and a tension force of 1000 N apply to it?V= √ Ft/e

Answer 1

Given:

the length of the cable is

$l=5\text{0 m}$

the mass of the cable is

$m=200\text{ kg}$

the tension force on the cable is

$T=1000\text{ N}$

Required: velocity of the wave.

Explanation:

to find the velocity of the wave on a cable we use the formula that is given by

$v=\sqrt[2]{\frac{T}{\mu}}$

Where

$T$

is the tension force and

$\mu$

is mass per unit length.

first, we calculate the mass per unit length.

$\begin{gathered} \mu=\frac{200\text{ kg}}{50\text{ m}} \\ \mu=4\text{ kg/m} \end{gathered}$

now put this value in the above relation and solve for velocity, we get

$\begin{gathered} v=\sqrt[2]{\frac{T}{\mu}} \\ v=\sqrt[2]{\frac{1000\text{ N}}{4\text{ kg/m}}} \\ v=15.81\text{ m/s} \end{gathered}$

Thus, the speed of the wave is 15.81 m/s.