Question

A wire of length 2.00 m fixed at both the ends is stretched to a tension of 160 N. if the fundamental frequency of vibration is 100 Hz, find its linear mass density.

• A. $1kg{m}^{-1}$
• B. $1g{m}^{-1}$
• C. ${10}^{-3}g{m}^{-1}$
• D. $10kg{m}^{-1}$

Answer 1

The correct option is B $1g{m}^{-1}$

Fundamental frequency is given by $\frac{v}{2L}$

$f=\frac{v}{2L}=\frac{1}{2L}\sqrt{\frac{T}{\mu }}$

$100=\frac{1}{2\times 2}\sqrt{\frac{160}{\mu }}\Rightarrow 400=\sqrt{\frac{160}{\mu }}\Rightarrow 160000=\frac{160}{\mu }$

$\mu =\frac{160}{160000}=\frac{1}{1000}={10}^{-3}kg{m}^{-1}$

$=1g{m}^{-1}$