A string of length 'L' is fixed at both ends . It is vibrating in its ` 3rd` overtone with maximum amplitude 'a'. The amplitude at a distance `L//3` from one end is

Options

A. a
B. 0
C. `(sqrt(3)a)/(2)`
D. `(a)/(2)`

Answer

C

Explanation

For a string vibrating in its `n^(th)`overtone (`(n + 1)^(th)` harmnonic)
`y = 2 A sin (((n+1)pix)/L) cos omegat`
For `x = (l)/(3), 2A = a` and n = 3, y = `[asin((4pi)/(l),(l)/(3))] cos omegat`
`asin"(4pi)/(3)cos omegat = -a((sqrt(3))/(2))cos omegat`