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 `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)))`

Answer

B

Explanation

`T_(1)=m_(2)g`
`T_(2)` at top `=(m_(1)+m_(2))g`
wavelength `(lambda)=(v)/(f)`
and `v=sqrt((T)/(mu))`
`T rarr` Tension in the spring
`mu rarr` Mass per unit length of the rope
`therefore lambda=(1)/(f)sqrt((T)/(mu))implieslambdapropsqrt(T)`
`(lambda_(2))/(lambda_(1))=sqrt((T_(2))/(T_(1)))=sqrt((m_(1)+m_(2))/(m_(2)))`.