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 $900\, N$. The wire resonates at a frequency of $500 \,Hz$. The next higher frequency at which the same wire resonates is $550\, Hz$. The length of the wire is $m$

Answer 1

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