Question

A uniform wire of linear density $0.004kg{m}^{-1}$ when stretched between two rigid supports with a tension $3.6\times {10}^{2}N$, resonates with a frequency of $420Hz$. The next harmonic frequency with which the wire resonates is $490Hz$. The length of the wire in metres is

• A. $1.41$
• B. $2.14$
• C. $2.41$
• D. $3.14$

Answer 1

The correct option is B $2.14$

$f_1=\frac{n}{2l}\sqrt{\frac{T}{\mu }}$
$f_2=\frac{(n+1)}{2l}\sqrt{\frac{T}{\mu }}$
$f_2-f_1=\frac{1}{2l}\sqrt{\frac{T}{\mu }}$
$70=\frac{1}{2l}\sqrt{\frac{3.6\times {10}^2}{0.004}}=\frac{3\times {10}^2}{2l}$
$l=\frac{30}{14}=2.14m$