Which coefficient of elasticity is responsible for the propagation of a wave in a string?

Consider the situation shown in the figure. The force $F$ is equal to $m_2g/2$. If the area of cross-section of the string is $A$ and its Young's modulus is $Y$,find the strain developed in it. The string is light and there is no friction anywhere.

$A$ steel rod of diameter $1\,cm$ is clamped firmly at each end when its temperature is $25\,^{\circ}C$ so that it cannot contract on cooling. The tension in the rod at $0\,^{\circ}C$ is approximately ......... $N$ $(\alpha = 10^{-5}/\,^{\circ}C, Y = 2 \times 10^{11}\,N/m^2)$

The ratio of the lengths of two wires of the same material is $1:2$ and the ratio of their radii is $1:\sqrt{2}$. If they are stretched by the same force,what is the ratio of the increase in their lengths?

Increase in length of a wire is $1 \, mm$ when suspended by a weight. If the same weight is suspended on a wire of double its length and double its radius,the increase in length will be ........ $mm$.

Two wires of the same length and material are stretched by the same force. If their masses are in the ratio $3:4$,then the ratio of their elongations is