Write the equation for the speed of a transverse wave on a stretched string.

$A$ string of mass $2.5 \, kg$ is under some tension. The length of the stretched string is $20 \, m$. If the transverse jerk produced at one end of the string takes $0.5 \, s$ to reach the other end,the tension in the string is .... $N$

$A$ sitar wire is replaced by another wire of same length and material but of three times the earlier radius. If the tension in the wire remains the same,by what factor will the frequency change?

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 $,v$)

$A$ string of $7 \; m$ length has a mass of $0.035 \; kg$. If the tension in the string is $60.5 \; N$,then the speed of a wave on the string is .... $m/s$.

The linear mass density of a vibrating string is $1.3 \times 10^{-4} \ kg/m$. $A$ transverse wave is propagating on the string and is described by the equation $y = 0.021 \sin(x + 30t)$,where $x$ and $y$ are measured in meters and $t$ in seconds. The tension in the string is approximately: (in $N$)