A metal string is fixed between rigid supports. It is initially at negligible tension. It’s Young’s modulus …

Q: A metal string is fixed between rigid supports. It is initially at negligible tension. It’s Young’s modulus is ‘Y’ density is ρ and coefficient of linear expansion is α . It is now cooled through a temperature ‘t’, transverse waves will move along it with a speed.

(a) $ \displaystyle \sqrt{\frac{Y \alpha t}{\rho}} $

(b) $ \displaystyle Y \sqrt{\frac{ \alpha t}{\rho}} $

(c) $\displaystyle \alpha \sqrt{\frac{Y t}{\rho}} $

(d) $\displaystyle t \sqrt{\frac{\rho}{Y \alpha}} $

Ans: (a)