Question

A rope with a mass density of 1 kg/m has one end tied to a vertical support. You hold the other end so that the rope is horizontal and has a tension of 4 N. If you move the end of the rope back and forth, you produce a transverse wave in the rope with a wave speed of 2 m/s. If you double the amount of tension you exert on the rope, what is the wave speed?

Answer 1

`v' = 2.83 m/s`

Step-by-step explanation:

Velocity of wave in stretched string is given by the formula

`v = \sqrt{(T)/(\mu)}`

here we know that

T = 4 N

also we know that linear mass density is given as

`\mu = 1 kg/m`

so we have

`v = \sqrt{(4)/(1)} = 2 m/s`

now the tension in the string is double

so the velocity is given as

`v' = \sqrt{(8)/(1)} = 2\sqrt2 m/s`

`v' = 2.83 m/s`