The length of a sonometer wire between two fixed ends is 110cm. Where should the two bridges the placed so as to divide the wire into three segments, whose fundamental frequencies are in the ration` 1:2:3?`

Options

A. 60cm, 30cm and 20cm
B. 20cm, 30cm and 60cm
C. 30cm, 20cm and 60cm
D. 60cm, 20cm and 30cm

Answer

A

Explanation

`l_1+l_2+l_3=110`
`n_1/n_2=l_2/l_1 therefore l_2/l_1 = 1/2 therefore l_2=l_1/2`
and `n_1/n_3 = l_3/l_1 therefore l_3=(l_1)/(3)`
`l_1+(l_1)/(2) +(l_1)/(3) = 110`
`6l_1+3l_1+2l_1=110xx6`
`11l_1 = 110xx6`
`l_1=60cm`
Similarly `l_2=30 " and " l_3 =20cm`