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

Answer:

$v' = 2.83 m/s$

Explanation:

Velocity of wave in stretched string is given by the formula

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

here we know that

T = 4 N

also we know that linear mass density is given as

$\mu = 1 kg/m$

so we have

$v = \sqrt{\frac{4}{1}} = 2 m/s$

now the tension in the string is double

so the velocity is given as

$v' = \sqrt{\frac{8}{1}} = 2\sqrt2 m/s$

$v' = 2.83 m/s$