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. At 36cm and 84 cm from one end
B. At 24cm and 72 cm from one end
C. At 48 cm and 96 cm from one end
D. At 72cm and 96 cm from one end

Answer

D

Explanation

Total length of the wire, L=114 cm
`n_1:n_2:n_3=1:3:4`
Let `L_1,L2 and L_3` be the lengths of the three parts
as `n prop 1/L`
`thereforeL_1:L_2:L_3=1/1:1/3:1/4=12:4:3`
`therefore L_1=(12/(12+4+3)times114)=72cm`
`L_2=(4/19 times 114)=24 cm`
and `L_3=(3/19 times 114)=18 cm`
Hence the bridges should be placed at 72 cm and 72+2=96 cm from one end.