Question

A wire having a linear mass density $5.0\times 10^{-3}kg/m$ is stretched between two rigid supports with a tension of $450N.$ The wire resonates at a frequency of $420Hz$. The next higher frequency at which the same wire resonates is $480Hz$. Find the length of the wire.

• A. 5 m
• B. 2.5 m
• C. 1.5 m
• D. 25 m

Answer 1

Answer: (B)

Suppose the wire vibrates at $420Hz$ in its nth harmonic and at $490Hz$ in its $(n+1)$ th harmonic.
$420=\frac{n}{2L}\sqrt{\frac{T}{\mu }}$ ...(i)
and $490=\frac{(n+1)}{2L}\sqrt{\frac{T}{\mu }}$ ...(ii)
Subtracting equation (i) from (ii)
$\frac{1}{2L}\sqrt{\frac{T}{\mu }}=60$
$\Rightarrow L=\frac{1}{2\times 60}\sqrt{\frac{T}{\mu }}$
$\therefore L=\frac{1}{2\times 60}\sqrt{\frac{450}{5\times 10^{-3}}}$
$=2.5m$