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 v = $\sqrt {T/μ}$, where T is the tension and μ is the linear mass density (mass per unit length) of the string. As the mass and length of the string are not changing, only the tension is increasing to 2T. Plugging this new tension into the equation for wave speed, we get v' = $\sqrt {(2T)/μ}$ = $\sqrt {2(T/μ)}$ = $\sqrt {2}$v. Therefore, the speed of the wave in the string is increased by a factor of $\sqrt {2}$ when the tension is doubled.

When a Certain String Is Under Tension T,the Speed of a Wave