Explanation:
Frequency of wave produced in the wire
\(n = \frac{1}{{2l}} \times \sqrt {\frac{T}{\mu }} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( 1 \right)\)
where \(l=\) length of the wire
\(T = \) tension in the wire
\(\mu=\) mass per unit length
Frequency produced when tension changes to \(4T\) is
\({n^\prime } = \frac{1}{{2l}} \times \sqrt {\frac{{4T}}{\mu }} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( 2 \right)\)
On dividing eq.(1) by eq.(2), we get
\(\dfrac{n}{n^{\prime}}=\sqrt{\dfrac{1}{4}}=\dfrac{1}{2} \Rightarrow n^{\prime}=2 n\)
