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Question

The length of a sonometer wire AB is 110 cm. Where should the two bridges be placed (from A) to divide the wire into 3 segments, whose fundamental frequencies are in the ratio of 1:2:3 ?

A
30 cm and 90 cm
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B
40 cm and 80 cm
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C
60 cm and 90 cm
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D
30 cm and 60 cm
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Solution

The correct option is C 60 cm and 90 cm
Fundamental frequency,
f=V2Lf1L
Given :
f1:f2:f3=1:2:3
1L1:1L2:1L3=1:2:3

L1:L2:L3=11:12:13
L1:L2:L3=6:3:2

Let L1=6x,L2=3x,L3=2x

Total length of sonometer wire =110 cm
L1+L2+L3=110
6x+3x+2x=110
x=10
L1=60 cm, L2=30 cm, L3=20 cm
Hence, bridges should be placed at distance of 60 cm and 90 cm from A.

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