When a certain string is under tension T, the speed of a wave in the string is v. What will be the speed of a wave in the string if the tension is increased to 2T without changing the mass or length of the string?
A)v/2
B)v/ $\sqrt { 2 }$
C)v $\sqrt { 2 }$
D)2v
E)4v

Question

Quizplus · Accepted Answer

The speed of a wave on a string is given by the formula $ v = \sqrt{\frac{T}{\mu}} $, where $ T $ is the tension and $ \mu $ is the linear mass density. If the tension is increased to 2T, the new speed $ v' $ is $ v' = \sqrt{\frac{2T}{\mu}} = \sqrt{2} \cdot \sqrt{\frac{T}{\mu}} = v \sqrt{2} $.

When a Certain String Is Under Tension T, the Speed 2\sqrt { 2 }2​

When a Certain String Is Under Tension T, the Speed $\sqrt { 2 }$