Three resonant frequencies of string with both rigid ends are 90, 150 and 210 Hz. If the length of the string is 80 cm, what is the maximum possible speed of the transverse wave in the 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`.