A non-uniform rope of length l hangs from a ceiling.Mass per unit length of rope `(mu)` changes as `mu=mu_0e^y`, where y is the distance along the string from its lowest point.Then graph between square of velocity of wave and y will be best represented as :

Options

A.
B.
C.
D. None of these

Explanation

`v_y=sqrt((T_y)/(mu_y))`
`T_y={underset(0)overset(y)intmu_0e^ydy}g`
`T_y=mu_0(e^y-1).g`
`v_y=sqrt(g-g/e^y)`
`v_y^2=g(1-e^-y)`