A sonometer wire has a length of 114 cm between its two fixed ends. Where should the two bridges be places so as to divide the wire into three segments, whose fundamental frequencies are in the ratio `1:3:4?`

Explanation

`l_(1) + l_(2) + l_(3) = 114 `
`n_(1) = (1)/(2l_(1)) sqrt(T//m),`
`n_(2) = (1)/(2l_(2)) sqrt(T//m),`
`n_(3) = (1)/(2l_(3)) sqrt(T//m),`
`n_(1) : n_(2) : n_(3) = 1: 3: 4`
`(n_(2))/(n_(1)) = (l_(1))/(l_(2)) =3 , or l_(2) = (l_(1))/(3)`
Similarly, `l_(3) = (l_(1))/(4)`
`rArr l_(1) = (l_(1))/(3) + (l_(1))/(4) = 114 `
or, `l_(1) = 72 cm, l_(2) = 24 cm, l_(3) = 18 cm `