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Question

A wire (fixed at both ends) of length l having tension T and radius r vibrates with natural frequency f. Another wire of same metal with length 2l having tension 2T and radius 2r will vibrate with natural frequency

A
f
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B
2f
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C
22f
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D
f22
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Solution

The correct option is D f22
Natural frequency for a wire with both ends fixed.
f=v2L=12LTμ
Mass per unit length (μ)=ρs
where ρ density of wire and s cross - section
f=12LTπr2ρ
fTLr
Let f2 be frequency of second string, then
ff2=T2T×2LL×2rr
ff2=42
f2=24f=f22

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