Question

A wire of length $200m$ is stretched to a tension of $160N$. If the fundamental frequency of vibration is $100Hz$, find its linear mass density.

Answer 1

Step 1. Given data

Length wire of $200m$

Tension of $160N$.

Fundamental frequency of vibration is $100Hz$

Step 2. Calculating linear mass density

Fundamental frequency $=f=\frac{1}{2L}x\sqrt{\frac{T}{m}}$

Where, $L$ is the length of wire

$T$ is the tension of wire

$m$ is the linear mass density

By substituting the given values, we get

$$\begin{gathered} 100=\frac{1}{2\times 2}\sqrt{\frac{160}{m}} \\ 100=\frac{1}{4}\sqrt{\frac{160}{m}} \\ m=1\times {10}^{-3}\raisebox{1ex}{$Kg$}\!\left/ \!\raisebox{-1ex}{$m$}\right. \end{gathered}$$

So, the linear mass density of the wire is $1\times {10}^{-3}K\raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$m$}\right.$.