$A$ 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:

$A$ 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 $g = 10 \ ms^{-2}$):

$A$ 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

$A$ $43\, m$ long rope of mass $5.0\, kg$ joins two rock climbers. One climber strikes the rope and the second one feels the effect $1.4\, s$ later. What is the tension in the rope in $N$?

$A$ uniform rope of length $12 \ m$ and mass $6 \ kg$ hangs vertically from a rigid support. $A$ block of mass $2 \ kg$ is attached to the free end of the rope. $A$ transverse pulse of wavelength $0.06 \ m$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is (in $m$)

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: