The extension in a string, obeying Hook's law is $x$. The speed of sound in the stretched string is

Question

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

Professor PC Thomas Classes · Answer

Speed $v \propto \sqrt{T}$. $T \propto x$. $v \propto \sqrt{x}$. If $x \rightarrow 1.5x$, $v \rightarrow 1.22v$.