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))`

Answer

B

Explanation

`V= sqrt((T )/( mu )) implies V_(1) = sqrt((m_(2) g)/( mu ))`
` implies V_(2) = sqrt((((m_(1) + m_(2))g))/( mu ))`
` V= f lamda `
` lamda prop V `
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`( lamda _(1))/( lamda_(2))=(V_(1))/(V_(2))`
`(lamda _(2))/( lamda_(1)) = sqrt((m_(1)+m_(2))/( m_(2)))`