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Q.

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 500Hz. The next higher frequency at which the same wire resonates is 550 Hz. The length of the wire is _______ m.

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answer is 10.

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Detailed Solution

Linear mass density $μ = 9.0 \times 10^{- 4} \frac{k g}{m}$
Tension, $T = 900 N$
Velocity of wire, $V = \sqrt{\frac{T}{μ}} = \sqrt{\frac{900}{9 \times 10^{- 4}}} = 10^{3} m / s$
$f_{n} = \frac{n V}{2 l} = 500.... (i)$
And $(n + 1) v = 500.... (i i)$
From (i) & (ii), $f_{n + 1} - f_{n} = \frac{v}{2 l} = 50$

$∴ l = \frac{10^{3}}{2 \times 50} = 10 m$

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