$A$ transverse wave is passing through a string as shown in the figure. The mass density of the string is $1 \ kg/m^3$ and the cross-sectional area of the string is $0.01 \ m^2$. The equation of the wave in the string is $y = 2 \sin(20t - 10x)$. The hanging mass is (in $kg$):-

$A$ string of mass $2.5\ kg$ is under a tension of $200\ N$. The length of the stretched string is $20.0\ m$. If a transverse jerk is struck at one end of the string,the disturbance will reach the other end in .... $\sec$.

$A$ 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 $\,s$)

$A$ uniform metal wire of length $L$,mass $M$,and density $\rho$ is under a tension $T$. If the speed of a transverse wave along the wire is $V$,then the area of cross-section of the wire is:

As shown in the figure, a block of mass $9 \, kg$ is hung by a wire of area of cross-section $1 \, mm^2$ in a lift going up with an acceleration of $2 \, ms^{-2}$. If the speed of the transverse wave on the wire is $120 \, ms^{-1}$, the density of the material of the wire is (Acceleration due to gravity $= 10 \, ms^{-2}$)

The equation of a transverse wave propagating on a stretched string is given by $y = 3 \sin (4x + 200t)$,where $x$ and $y$ are in metres and the time $t$ is in seconds. If the tension applied to the string is $500 \ N$,the linear density of the string is: (in $kg \ m^{-1}$)