A sonometer wire of length 114 cm is fixed at both the ends. Where should the two bridges be placed so as to divide the wire into three segments whose fundamental frequencies are in the ratio `1 : 3 : 4`?

Options

A. 24cm and 72cm
B. 72cm and 96cm
C. 18cm and 72cm
D. 18cm and 24cm

Answer

B

Explanation

`l_1+ l_2+l_3 = 114, " " n_1l_1 = n_2l_2 therefore l_2=(l_1)/(3)`
`n_1l_1=n_3l_3 therefore l_3 = (l_1)/(4)`
`l_1+(l_1)/(3)+(l_1)/(4) = 114`
`19l_1=114xx12`
`l_1=72cm`
Similarly `l_2=96cm`