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A wire having a linear mass density of 5.0 × 10–3 kg/m is stretched between two rigid supports with a tension of 450 N. The wire resonates at a frequency of 420 Hz. The next higher frequency at which the same wire resonates is 490 Hz. Find the length of the wire. 

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Suppose Pth and (P + 1)th be the number of loops corresponding to the resonance frequencies 420 Hz and 490 Hz respectively. Then

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