A stretched string of length ` 1 m` fixed at both ends , having a mass of `5 xx 10^(-4) kg` is under a tension of `20 N`. It is plucked at a point situated at `25 cm` from one end . The stretched string would vibrate with a frequency of

Options

A. 100 Hz
B. 150 Hz
C. 200 Hz
D. 250 Hz

Answer

C

Explanation

When it is plucked at 25 cm or a distance of `L/4`, the wire will vibrate with 2 loops.
` :. 2 ( lambda/2) = L `
` :. lambda = L = 1 ` m
and mass per unit length ` = (0.5 g)/(1 m) = 5 xx 10^(-4) ` kg/m
` :. N = 1/lambda sqrt(T/m) = 1/L sqrt(T/ m) `
` = 1/1 sqrt(20/(5 xx 10^(-4))) = sqrt( 4 xx 10^(4)) `
` = 2 xx 10^(2) = 200 ` Hz