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.)

Options

A. 20m
B. 80m
C. 40m
D. 60m

Answer

b

Explanation

Given, `y = 0.3 sin (0.157 x) cos (200 pit)`
So, k= 0.157 and `omega = 200pi =2pif`
`:.` F= 100Hz and `v= (omega)/(k) = (200pi)/(0.157)= 400m//s`
Now, using `f= (nv)/(2l)= (4v)/(2l)= (2v)/(l)` [here n= 4]
`:. L= (2v)/(f)= (2 xx 400)/(100)= 80 m`