A wave pulse starts propagating in $+x$-direction along a non-uniform wire of length $10 \mathrm{m}$ with mass per unit length given $m=m_0+\alpha x$ and under a tension of $100 \mathrm{N}$. Find the time taken by the pulse to travel from the lighter end $(x=0)$ to the heavier end ($m_0={10}^{-2} \mathrm{kg} {\mathrm{m}}^{-1}$ and $\alpha =9\times {10}^{-3} \mathrm{kg} {\mathrm{m}}^{-2}$)

The speed of sound in an elastic string when it is extended by $x \mathrm{m}$ is $v.$ If it is further extended to $3x \mathrm{m},$ the speed of the sound becomes $\underline{ }$

A transverse wave propagating on a stretched string of linear density $3\times {10}^{-4} {\mathrm{kgm}}^{-1}$ is represented by the equation

$y=0.2\sin (1.5x+60t)$

where, $x$ in metres and $t$ is in seconds. The tension in the string (in Newton) is