A uniform metal wire has length \(L\), mass \(M\) and density \(\rho\). It is under tension \(T\) and \(v\)…
A uniform metal wire has length \(L\), mass \(M\) and density \(\rho\). It is under tension \(T\) and \(v\) is the speed of transverse wave along the wire. The area of cross-section of the wire is
\(\frac{T}{v^2 \rho}\)
\(\frac{v^2 \rho}{T}\)
\(T^2 \rho V\)
\(T v^2 \rho\)
Solution
The speed of transverse wave along a wire is given by
\(v=\sqrt{\frac{T}{\mu}}\)
where, \(\mu=\) mass per unit length.
\(=\) volume of unit length \(\times\) density
\(=\) area \(\times\) density
\(\therefore \quad v=\sqrt{\frac{T}{A \rho}} \Rightarrow A=\frac{T}{v^2 \rho}\)
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