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. 1 kg m^-1
• B. 1 gm^-1
• C. 10^-3gm^-1
• D. 10 kgm^-1

Answer 1

The correct option is B

1 gm^-1

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

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

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

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

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