Question

The string in FIGURE P16.60 has linear density $\mu$. Find an expression in terms of M, $\mu$, and $\theta$for the speed of waves on the string.

Short answer

Speed of the waves on the string is,$v=\sqrt{\frac{Mg\sin \theta }{\mu }}$

Step-by-step solution

Introduction

The string has a linear density of $\mu$

Mass of the block is$M$

If we consider the string has a tension force of $T$then the speed can be determined by,

role="math" localid="1648892786316" $v=\sqrt{\frac{T}{\mu }}$

Determination of the speed

Tension of the string $\left(T\right)=$Weight component directed downward the slope.

Now, component of weight directed downward the slope is,

$T=Mg\sin \theta$

Thus, the speed of waves on the string is,

$$\begin{gathered} v=\sqrt{\frac{T}{\mu }} \\ v=\sqrt{\frac{Mg\sin \theta }{\mu }} \end{gathered}$$