$A$ uniform rope of mass $0.1 \,kg$ and length $2.45 \,m$ hangs from a rigid support. The time taken by a transverse wave formed in the rope to travel through the full length of the rope is (Assume $g = 9.8 \,m/s^2$). (in $\,s$)

When the area of cross-section of a stretched wire is halved and tension is doubled,the speed of propagation of transverse waves along it becomes $k$ times the initial speed. Then,$k$ is:

$A$ pulse is generated at the lower end of a hanging rope of uniform density and length $L$. The speed of the pulse when it reaches the midpoint of the rope is:

$A$ string of mass $2.50 \;kg$ is under a tension of $200\; N$. The length of the stretched string is $20.0 \;m$. If the transverse jerk is struck at one end of the string,how long (in $sec$) does the disturbance take to reach the other end?

$Assertion :$ Two waves moving in a uniform string having uniform tension cannot have different velocities.
$Reason :$ Elastic and inertial properties of string are same for all waves in same string. Moreover,the speed of a wave in a string depends on its elastic and inertial properties only.

$A$ 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: