A `1 m` long rope, having a mass of `40 g`, is fixed at one end and is tied to a light string at the other end. The tension in the string in `400 N`. Find the wavelength in second overtone (in `cm`).

Answer

80

Explanation

`L = 1 m`
`M = 0.04 kg`
`mu = (M)/(L) = 0.04 kg//m :. V sqrt((T)/(mu)) = sqrt((400)/(0.04)) = 100 m//sec`
For foundamental frequency
`L = (lambda)/(4) rArr lambda = 4L = 4 m`
`:. f_(1) = (10C)/(4) = 25 Hz`
(i) `(lambda_(1))/(4) = L = 1`
`lambda_(1) = 4 m`
(ii) `(3lambda_(2))/(4) = L = 1`
`lambda_(2) = (4)/(3) m`
(iii) `(5lambda_(3))/(4) = L`
`lambda_(3) = (4)/(5) m`