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 = $\sqrt { T/\mu }$, where T is the tension and \mu is the linear mass density. 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' = $\sqrt { T/(\mu/2) } = \sqrt { 2T/\mu } = v \sqrt { 2 }$.

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