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A wire having a linear mass density 5.0 ...

A wire having a linear mass density `5.0 xx 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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To find the length of the wire, we can follow these steps: ### Step 1: Understand the relationship between the frequencies and the number of loops The frequencies at which the wire resonates are related to the number of loops (or harmonics) formed in the wire. Let: - \( f_1 = 420 \, \text{Hz} \) (first frequency) - \( f_2 = 490 \, \text{Hz} \) (next higher frequency) Let \( p \) be the number of loops corresponding to the frequency \( f_1 \), then the number of loops corresponding to \( f_2 \) will be \( p + 1 \). ...
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