Question

A wire having a linear mass density $9.0\times 10^{-4}kg/m$ is stretched between two rigid supports with a tension of $900N$. The wire resonates at a frequency of $500Hz$. The next higher frequency at which the same wire resonates is $550Hz$. The length of the wire is $m$

Answer 1

Answer: 10

$\mu =9.0\times 10^{-4}\frac{kg}{m}$
$T=900N$
$V=\sqrt{\frac{T}{\mu }}=\sqrt{\frac{900}{9\times 10^{-4}}}=1000m/s$
$f_1=500Hz$
$f=550$
$\frac{nV}{2\ell }=500\dots (i)$
$\frac{(n+1)V}{2\ell }=500\dots (ii)$
(ii) (i) $\frac{V}{2\ell }=50$
$\ell =\frac{1000}{2\times 50}=10$