Four wires of identical length, diameters and of the same material are stretched on a sonometer wire. If the ratio of their tension is 1:4:9:16, then the ratio of their fundamental frequencies is
A
16:9:4:1
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B
4:3:2:1
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C
1:4:2:16
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D
1:2:3:4
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Solution
The correct option is D1:2:3:4 A sonometer wire is stretched between two fixed wedges. ⇒ Fundamental frequency of vibration, f=v2L=12L√Tμ ⇒f∝√T
Ratio of frequencies in wires considered is ∴f1:f2:f3:f4=√T1:√T2:√T3:√T4
Given that T1:T2:T3:T4=1:4:9:16 ∴f1:f2:f3:f4=√T1:√T2:√T3:√T4=1:2:3:4