Question

The wave speed on a string under tension is 200 m/s. What is the speed if the tension is halved?

Short answer

The new speed of the wave is 141.4 m/s

Step-by-step solution

Step 1. Write the given information

The speed of the wave is given as v= 200m/sec

Thereafter, the tension (T) of the string is halved.

Step 2. To determine the speed of wave when tension is halved

The formula for the speed is given as

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

Here µ is the effective mass of the string

The tension is halved,

$T\to \frac{T}{2}$

The new speed is given as

$$\begin{gathered} v=\sqrt{\frac{\left(T/2\right)}{\mu }}=\frac{1}{\sqrt{2}}\left(\sqrt{\frac{T}{\mu }}\right) \\ v=\frac{200}{\sqrt{2}}=141.4m/s \end{gathered}$$
Thus, the new speed of the wave is 141.4 m/s