$A$ heavy uniform rope is suspended vertically from a ceiling and is in equilibrium. $A$ pulse is generated at the bottom end of the rope as shown. As the pulse travels up the rope,its acceleration at any instant is ($g$ is acceleration due to gravity).

$A$ sitar wire is replaced by another wire of same length and material but of three times the earlier radius. If the tension in the wire remains the same,by what factor will the frequency change?

$A$ string of mass $0.1 \, kg$ is under a tension $1.6 \, N$. The length of the string is $1 \, m$. $A$ transverse wave starts from one end of the string. The time taken by the wave to reach the other end is (in $s$.)

$A$ uniform rope of length $L$ and mass $m_1$ hangs vertically from a rigid support. $A$ block of mass $m_2$ is attached to the free end of the rope. $A$ transverse pulse of wavelength $\lambda_1$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is $\lambda_2$. The ratio $\lambda_2 / \lambda_1$ is:

The equation of a travelling wave on a stretched string of linear mass density $5 \, g/m$ is $y = 0.03 \sin(450t - 9x)$,where distance and time are measured in $SI$ units. The tension in the string is ... $N$.

$A$ 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?