Three consecutive resonant frequencies of a string are `90, 150` and `210 Hz`. If the length of the string is `80 cm`, what would be the seed (in `m//s`) of a transverse wave on this string ?

Answer

96

Explanation

`(n)/(2l) sqrt((T)/(mu)) = 90`
`(n + 1)/(2l) sqrt((T)/(mu)) = 150 , (n + 2)/(2l) sqrt((T)/(mu)) = 210`
`therefore (n)/(n + 1) = (90)/(150) rArr n = 1.5`
`therefore`
`therefore (n)/(2l) sqrt((T)/(mu)) = 90 = (n)/(2l) V`
`(V)/(2l) = (90)/(n ) = (90)/(1.5) = 60`
`therefore (V)/(4l) = 30`
(b) `(3V)/(4L) = 90` and `(5V)/(4l) = 150`
and `(7V)/(4l) = 210`
(c) overtones are `1st, 2nd, 3rd`
(d) `(v)/(4 xx 0.8) = 30 rArr v = 96 m//sec`.