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A string of length 'L' is fixed at both ...

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

A

`a`

B

0

C

`(sqrt(3)a)/(2)`

D

`(a)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
For a string vibrating in its `n^(th)` overtong `((n+1)^(th) ` harmonic)
`y=2A sin (((n+1)pix)/(L))cos omegat`

For `x=(l)/(3),2A=a` and `n=3,`
`y=[a sin ((4pi)/(l).(l)/(3))]cos omegat`
`=a.sin((4pi)/(3))cos omegat`
`=-a.((sqrt(3))/(2))cos omegat`
`i.e.` at `x=(l)/(3), ` the amplitude is `(sqrt(3)a)/(2)`
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