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

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 wave length of the pulse when it reaches the top of the rope is $\lambda _2$. The ratio $\lambda _2\,/\,\lambda _1$ is 

Spacing between two successive nodes in a standing wave on a string is $x$ . If frequency of the standing wave is kept unchanged but tension in the string is doubled, then new spacing between successive nodes will  become

Mechanical waves on the surface of a liquid are

Two pulses travel in mutually opposite directions in a string with a speed of $2.5 cm/s$ as shown in the figure. Initially the pulses are $10cm$ apart. What will be the state of the string after two seconds

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 :