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25/01/2022 1:51 pm
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A wire having a linear mass density 9.0 × 10–4 kg/m 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.
1 Answer
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25/01/2022 1:57 pm
μ = 9.0 × 10–4 kg/m
T = 900 N
V = \(\sqrt{\frac{T}{μ}}\) = \(\sqrt{\frac{900}{9 \times 10^{-4}}}\)
= 1000 m/s
f1 = 500 Hz
f = 550
\(\frac{nV}{2 \ell}\) = 500 ......(i)
\(\frac{(n+1)V}{2 \ell}\) = 500 .....(ii)
(ii) (i)
\(\frac{V}{2 \ell}\) = 50
ℓ = \(\frac{1000}{2 \times 50}\) = 10