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?a. 2.8 m/s

b. 1.0 m/s
c. 2.0 m/s
d. 0.25 m/s
e. 4.0 m/s

Answer 1

Speed, v = 2.82 m/s

Step-by-step explanation:

It is given that,

Mass per unit length of the rope,
`\mu =(m)/(l)=1\ kg/m`

Tension, T = 4 N

Wave speed, v = 2 m/s

Let v' is the speed of the wave when there is tension is doubled. The wave speed is given by :

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

If tension is doubled, means, T = 8 N

`v=\sqrt{(8)/(1)}`

v = 2.82 m/s

So, if the tension is doubled, the wave speed 2.8 m/s. Hence, this is the required solution.