A 2.00 m-long rope, having a mass of 80 g, is fixed at one end and is tied to a light string at the other end. The tension in the string is 256 N. (a) Find the frequencies of the fundamental and the first two overtones. (b) Find the wavelength in the fundamental and the first two overtones.

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`