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 $,v$)

$A$ transverse wave propagating on a stretched string of linear density $3 \times 10^{-4} \ kg \ m^{-1}$ is represented by the equation $y = 0.2 \sin (1.5 x + 60 t)$, where $x$ is in metres and $t$ is in seconds. The tension in the string (in newton) is

$A$ string of mass $M$ and length $L$ hangs freely from a fixed point. The velocity of a transverse wave along the string at a distance $x$ from the free end will be:

$A$ rope of length $L$ and mass $M$ hangs freely from the ceiling. If the time taken by a transverse wave to travel from the bottom to the top of the rope is $T$,then the time taken to cover the first half length is:

$A$ string wave equation is given by $y=0.002 \sin (300 t-15 x)$ and the linear mass density is $\mu=0.1 \ kg/m$. Find the tension in the string (in $N$).

$A$ steel wire with mass per unit length $7.0 \times 10^{-3} \, kg \, m^{-1}$ is under tension of $70 \, N$. The speed of transverse waves in the wire will be $......... \, m/s$.