$A$ string of length $L$ and mass $M$ hangs freely from a fixed point. The velocity of transverse waves along the string at a distance $x$ from the free end is

$A$ 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 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 $kg \ m^{-1}$)

If the initial tension on a stretched string is doubled,then the ratio of the initial and final speeds of a transverse wave along the string is:

In the figure shown,a mass of $1 \ kg$ is connected to a string of mass per unit length $1.2 \ g/m$. The length of the string is $1 \ m$ and its other end is connected to the ceiling of a lift which is accelerating upwards with an acceleration of $2 \ m/s^2$. $A$ transverse pulse is produced at the lowest point of the string. The time taken by the pulse to reach the top of the string is .... $s$. (Take $g = 10 \ m/s^2$)

The fundamental frequency of vibration of a string stretched between two rigid supports is $50\,Hz$. The mass of the string is $18\,g$ and its linear mass density is $20\,g/m$. The speed of the transverse waves produced in the string is $..........\,m/s$.