A transverse wave is travelling with velocity ' $\mathrm{V}^{\prime}$ through a metal wire of length '…
A transverse wave is travelling with velocity ' $\mathrm{V}^{\prime}$ through a metal wire of length ' $\mathrm{L}$ '
and density ' $\rho$ '. The tensile stress in the wire is
$\mathrm{V} \rho^{2}$
$\frac{\mathrm{v}^{2}}{\rho}$
$\frac{\rho}{\mathrm{V}^{2}}$
$\mathrm{~V}^{2} \rho$
Solution
$\mathrm{V}=\sqrt{\frac{T}{m}}$ where $\mathrm{T}$ is the tension and $\mathrm{m}$ is mass per unit length.
$\mathrm{m}=\mathrm{A} . p$ where $\mathrm{A}$ is an area of cross-section.
$\therefore V=\sqrt{\frac{T}{A \rho}}$
$\therefore V^{2}=\frac{T}{A \rho}$
$\therefore \frac{T}{A}=V^{2} \rho$
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