Question

A string of mass m 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 mass of the string is increased to 2m but with no change in the length or tension?
A) v/ sq. rt. of 2
B) v/2
C) 2v
D) v * sq. rt. of 2
E) 4v

Answer 1

Explanation:

Below is an attachment containing the solution.

Answer 2

Answer:

A) v/ sq. rt. of 2

Explanation:

The speed of the wave in the string is defined as:

$v=\sqrt{\frac{T}{\mu}}$

Where T is the tension on the string and $\mu$ is the linear density, that is, the mass per unit length:

$\mu=\frac{m}{L}$

Where m is the mass of the string and L its length. We have $m'=2m$, $T'=T$ and $L'=L$:

$v'=\sqrt\frac{T'}{m'/L'}\\v'=\sqrt\frac{T}{2m/L}\\v'=\frac{1}{\sqrt2}\sqrt\frac{T}{m/L}\\v'=\frac{v}{\sqrt2}$