$A$ string of mass $0.2 \ kg$ is under a tension of $2.5 \ N$. The length of the string is $2 \ m$. $A$ transverse wave starts from one end of the string. The time taken by the wave to reach the other end is: (in $s$)

$A$ 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 wire $20 \,m$ long and weighing $50 \,N$ hangs vertically. The speed of the wave at the midpoint of the wire is (acceleration due to gravity $= g = 10 \,ms^{-2}$)

The speed of a wave on a string is $150 \,ms^{-1}$ when the tension is $120 \,N$. The percentage increase in the tension in order to raise the wave speed by $20 \%$ is

$A$ 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 $\,s$)

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 $N$)