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  4. A metal wire of linear mass density 9.8 g / m is stretched with a tension of 10 kg-wt between two rigid supports 1 m 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 v . The frequency v of alternating source is

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Q. A metal wire of linear mass density $9.8\, g / m$ is stretched with a tension of $10\, kg$-wt between two rigid supports $1 \,m$ 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 $v .$ The frequency $v$ of alternating source is

BHUBHU 2010

Solution:

Frequency, $f=\frac{1}{2 l} \sqrt{\frac{T}{\rho}}$
$=\frac{1}{2 \times 1} \sqrt{\frac{10 \times 9.8}{9.8 \times 10^{-3}}} $
$=\frac{1}{2} \sqrt{10^{4}} $
$=\frac{100}{2} $
$=50\, H z$