Question

If $ V $ is the velocity of wave in a rope having tension $ T $, find the velocity when the tension becomes $ 8T $.

• A. \( 8V \)
• B. \( \frac{V}{8} \)
• C. \( \sqrt{8}V \)
• D. \( V \)

Hint:

The velocity of a wave in a rope increases with the square root of the tension, so increasing the tension by a factor of 8 will increase the velocity by a factor of \( \sqrt{8} \).

Answer 1

The Correct Option is C

The velocity \( V \) of a wave in a rope is related to the tension \( T \) and the mass per unit length \( \mu \) of the rope by the formula: \[ V = \sqrt{\frac{T}{\mu}} \] If the tension is increased to \( 8T \), the new velocity \( V' \) will be: \[ V' = \sqrt{\frac{8T}{\mu}} = \sqrt{8} \times \sqrt{\frac{T}{\mu}} = \sqrt{8}V \]
Thus, the velocity when the tension becomes \( 8T \) is \( \sqrt{8V} \).