A metal wire of linear mass density of 9.8 g/m is stretched with a… | JEE Main 2003 (AIEEE)

Q108JEE Main 2003 · AIEEEMedium

Stationary Waves & Vibrating Strings

A metal wire of linear mass density of $9.8\text{ g/m}$ is stretched with a tension of $10\text{ kg-wt}$ between two rigid supports $1$ metre apart. The wire passes at its middle point between the poles of a permanent magnet, and it vibrates in resonance when carrying an alternating current of frequency $n.$ The frequency $n$ of the alternating source is

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Answer: (a)

Force on the wire at its middle excites the fundamental (antinode at the centre).
$T = 10 \times 9.8 = 98\text{ N}$ , $\mu = 9.8\times10^{-3}\text{ kg/m}$ , so $v = \sqrt{\dfrac{98}{9.8\times10^{-3}}} = 100\text{ m/s}$ .
$n = \dfrac{v}{2L} = \dfrac{100}{2\times1} = 50\text{ Hz}$
So the answer is (a) $50\text{ Hz}$ .

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