A wire having a linear mass density 9 . 0 × 10 - 4 kg m - 1 is stretched between two rigid supports with a tension of 900 N . The wire resonates at a frequency of 500 Hz . The next higher frequency at

Question

A wire having a linear mass density 9 . 0 × 10 - 4 kg m - 1 is stretched between two rigid supports with a tension of 900 N . The wire resonates at a frequency of 500 Hz . The next higher frequency at which the same wire resonates is 550 Hz . The length of the wire is ___________ m .

TestHub · Accepted Answer

f n = n v 2 ℓ = 500 f n + 1 = ( n + 1 ) v 2 ℓ = 550 n + 1 n = 11 10 Thus, n = 10 Thus, ℓ = nv 2 f n v = T μ = 10 2 × 500 × 900 9 × 10 - 4 = 10 m

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