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 C60 cm and 90 cm Fundamental frequency, f=V2L⇒f∝1L 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.