A uniform rope of legnth `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 `lamda_1` is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is `lamda_2`. The ratio `(lamda_2)/(lamda_1)` is

Options

A. `sqrt((m_(1))/(m_(2))`
B. `sqrt((m_(1) + m_(2))/(m_(2))`
C. `sqrt((m_(2))/(m_(1))`
D. `sqrt((m_(1) + m_(2))/(m_(1))`

Explanation

Tension at 1, `T_(1) = m_(2) g`
Tension at 2, `T_(2) = (m_(1) + m_(2)) g`
`v = f_(2) = sqrt(T//mu)`
`(lambda_(2))/(lambda_(1)) = sqrt((T_(2))/(T_(1))) = sqrt(((m_(1) + m_(2)) g)/(m_(2) g))`
`= sqrt((m_(1) + m_(2))/(m_(2)))`