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

Explanation

Wavelength of pulse at the lower end `(lambda_(1))prop` velocity `(v_(1))=sqrt((T_(1))/(mu))`
Similarly, `lambda_(2)propv_(2)=sqrt((T_(2))/(mu))`
`therefore (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)))`