A string of length L is under tension, and the speed of a wave in the string is v. What will be the speed of a wave in the string if the length is increased to 2L but with no change in the mass or tension?
A) v/2
B) v/ $\sqrt { 2 }$
C) v $\sqrt { 2 }$
D) 2v
E) 4v

Question

Quizplus · Accepted Answer

The speed of a wave in a string is given by:$$v = \sqrt{\frac{T}{\mu}}$$where T is the tension in the string and $\mu$ is the linear mass density of the string. If the length of the string is increased to 2L, the linear mass density will be reduced to $\mu/2$. Therefore, the speed of the wave will become:$$v' = \sqrt{\frac{T}{\mu/2}} = \sqrt{2}v$$

A String of Length L Is Under Tension, and the Speed