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
2√2f
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D
f2√2
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Solution
The correct option is Df2√2 Natural frequency for a wire with both ends fixed. f=v2L=12L√Tμ
Mass per unit length (μ)=ρs
where ρ→ density of wire and s→ cross - section ⇒f=12L√Tπr2ρ ⇒f∝√TLr
Let f2 be frequency of second string, then ∴ff2=√T2T×2LL×2rr ⇒ff2=4√2 ∴f2=√24f=f2√2