Question

A wire having a linear density $0.10kg/m$ is kept under a tension $490N$ it is observed that it resonates at a frequency of $400Hz$ and the next frequency $450Hz$. The length of the wire is

• A. $14m$
• B. $0.7m$
• C. $1.6m$
• D. $0.49m$

Answer 1

The correct option is B $0.7m$

Given-

$T=490N$

$\mu =0.1kg/m$

$f\left(n\right)=400Hz$

$f(n+1)=450Hz$

Velocity of waves on string is given by-

$v=\surd \left(T/\mu \right)$

$v=\surd \left(490/0.1\right)$

$v=70m/s$

Length of the wire cak be calculated by-

$l=n\lambda 1/2=(n+1)\lambda 2/2$

$n\times 70/400=(n+1)\times 70/450$

$45n=40n+40$

$n=8$

Substitute this in ,

$l=8\times 70/(400\times 2)$

$l=0.7m$

Therefore, length of the wire is $0.7m.$

Hence,

option $B$ is correct answer.