$A$ uniform thin rope of length $12 \, m$ and mass $6 \, kg$ hangs vertically from a rigid support and a block of mass $2 \, kg$ is attached to its free end. $A$ transverse short wavetrain of wavelength $6 \, cm$ is produced at the lower end of the rope. What is the wavelength of the wavetrain (in $cm$) when it reaches the top of the rope?

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 $N$)

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

$A$ 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 $N$).

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

$A$ block $M$ hangs vertically at the bottom end of a uniform rope of constant mass per unit length. The top end of the rope is attached to a fixed rigid support at $O$. $A$ transverse wave pulse (Pulse $1$) of wavelength $\lambda_0$ is produced at point $O$ on the rope. The pulse takes time $T_{OA}$ to reach point $A$. If the wave pulse of wavelength $\lambda_0$ is produced at point $A$ (Pulse $2$) without disturbing the position of $M$,it takes time $T_{AO}$ to reach point $O$. Which of the following options is/are correct?