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  • A metal string is fixed between rigid supports. It is initially at negligible tension. Its Young's modulus is Y, density is <span style="font-family:"Calibri

A metal string is fixed between rigid supports. It is initially at negligible tension. Its Young's modulus is Y, density is ρ, and coefficient of thermal expansion is α.  If it is now colled through a temperature = t, transverse  waves will move along it with speed

Option: 1

Y \sqrt{\frac{\alpha t}{\rho}}


Option: 2

\alpha t \sqrt{\frac{Y}{\rho}}


Option: 3

\sqrt{\frac{Y \alpha t}{\rho}}


Option: 4

\quad t \sqrt{\frac{Y \alpha}{\rho}}


Answers (1)

best_answer

\begin{gathered} \Delta l=l \alpha t \text { or } \frac{\Delta l}{l}=\alpha t \\ \text { stress }=Y \times \text { strain }=Y \alpha t \text { (also called thermal stress) } \end{gathered}\\\\\ \therefore Tension, T=Y s \alpha t\\\\ Now, \begin{aligned} & v=\sqrt{\frac{T}{\rho s}}=\sqrt{\frac{Y \alpha s t}{\rho s}} \\ & v=\sqrt{\frac{Y s t}{\rho}} \end{aligned}

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