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.

Step-by-step explanation:

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

`v=\sqrt[2]{(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]{(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.