If the tension and diameter of a sonometer wire of fundamental frequency n are doubled and density is halved, then its fundamental frequency will become
A
n4
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B
√2n
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C
n
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D
n√2
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Solution
The correct option is Cn Frequency of a sonometer wire n=12l√Tπr2ρ
As the tension and diameter of a sonometer wire are doubled and density is halved ρ′=ρ2;T′=2T and D′=2D⇒r′=2r
n′=12l
⎷2Tπ(2r)2ρ2=12l√Tπr2ρ=n.
Hence, the correct answer is option (c)