When the area of cross-section of a stretched wire is halved and tension is doubled,the speed of propagation of transverse waves along it becomes $k$ times the initial speed. Then,$k$ is:

The extension in a string obeying Hooke's law is $x$. The speed of sound in the stretched string is $v$. If the extension in the string is increased to $1.5x$,the speed of sound will be (in $,v$)

If the initial tension on a stretched string is doubled,then the ratio of the initial and final speeds of a transverse wave along the string is:

$A$ uniform string of length $20 \ m$ is suspended from a rigid support. $A$ short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the support is (take $g = 10 \ ms^{-2}$):

Two $Cu$ wires of radii $R_{1}$ and $R_{2}$ are such that $(R_{1} > R_{2})$. Then which of the following is true?

The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by $4\, \%$,will be ......... $\%$