A wire having a linear mass density 9.0 × 10 - 4 kg/m is stretched… | JEE Main 2021 (31 Aug, Shift 1)

Q76JEE Main 2021 · 31 AUG · SHIFT 1Easy

Stationary Waves & Vibrating Strings

A wire having a linear mass density 9.0 $\times$ 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.

Numerical answer type. Work it out, then open the answer.

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Answer: 10

Wave speed $v = \sqrt{\dfrac{T}{\mu}} = \sqrt{\dfrac{900}{9.0 \times 10^{-4}}} = \sqrt{10^6} = 1000\text{ m/s}$ .
Consecutive resonances differ by $f_0 = \dfrac{v}{2L}$ : $f_0 = 550 - 500 = 50\text{ Hz}$ .
$L = \dfrac{v}{2f_0} = \dfrac{1000}{2 \times 50} = 10\text{ m}$ .
So the length is $10\text{ m}$ .

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