String Waves Questions

Each of the two strings of length $51.6\text{cm}$ and $49.1\text{cm}$ are tensioned separately by $20\text{N}$ force. Mass per unit length of both the strings is same and equal to $1\text{g/m}$. When both the strings vibrate simultaneously, the number of beats is:

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: