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/sb. 1.0 m/sc. 2.0 m/sd. 0.25 m/se. 4.0 m/s

Answer 1

Answer: Option (a) is the correct answer.

Explanation:

The given data is as follows.

   mass per unit length ($\mu$) = $\frac{M}{l}$ = 1 kg/m

      Tension = 4 N

    Speed (v) = $\sqrt{\frac{F}{\mu}}$

So, when F is doubled then change in value of F will be as follows.

               F = 4 + 4 = 8 N

Therefore, speed will be calculated as follows.

           v = $\sqrt{\frac{8 N}{1 kg/m}}$

              = 2.8 m/s

Thus, we can conclude that the wave speed is 2.8 m/s.