$A$ transverse wave travels on a taut steel wire with a velocity of $v$ when the tension in it is $2.06 \times 10^{4} \; N$. When the tension is changed to $T$,the velocity changes to $v/2$. The value of $T$ is close to:

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 $kg \ m^{-1}$)

$A$ 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:

$A$ wire of variable mass per unit length $\mu = \mu_0 x$ is hanging from the ceiling as shown in the figure. The length of the wire is $l_0$. $A$ small transverse disturbance is produced at its lower end. Find the time after which the disturbance will reach the other end.

$A$ transverse wave is propagating on a string. The linear mass density of the vibrating string is $10^{-3} \ kg/m$. The equation of the wave is $Y = 0.05 \sin(x + 15t)$,where $x$ and $Y$ are in meters and time $t$ is in seconds. The tension in the string is: (in $N$)

$A$ uniform string is suspended vertically. $A$ transverse pulse is created at the top of the string. Then: