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A string is clamped at both the ends and...

A string is clamped at both the ends and it is vibrating in its `4^(th)` harmonic. The equation of the stationary wave is `Y=0.3 sin ( 0.157 x) cos (200 pi t)`. The length of the string is: (All quantities are in SI units.)

Text Solution

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Given y=0.3`sin (0.157x)cos (200pit)`
So k=0.157 and `omega=200pi=2pif`
`:.f=100` Hz and `v=(omega)/2=(200pi)/0.157=4000m//s`
Now using `f=(nv)/(2l)=(4v)/(2l)=(2v)/l` [here n=4]
`:.l=(2v)/f=(2xx4000)/100=80m`
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