Question

A wire of length 2⋅00 m is stretched to a tension of 160 N. If the fundamental frequency of vibration is 100 Hz, find its linear mass density.

Answer 1

Given:
Length of the wire (L)= 2.00 m
Fundamental frequency of the vibration (f₀) = 100 Hz
Applied tension (T) = 160 N

$$\begin{gathered} \text{Fundamental frequency,}{f}_0=\frac{1}{2L}\sqrt{\left(\frac{T}{m}\right)} \\ \Rightarrow 10=\frac{1}{4}\sqrt{\frac{160}{m}} \\ \Rightarrow m=1\times {10}^{-3}\mathrm{kg}/\mathrm{m} \\ \Rightarrow m=1\mathrm{g}/\mathrm{m} \end{gathered}$$
So, the linear mass density of the wire is 1 g/m.