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  4. A metal wire of linear mass density of 9.8 g m- 1 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 n . The frequency n of the alternating sources is

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Q. A metal wire of linear mass density of $9.8 \, g \, m^{- 1}$ 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 $n$ . The frequency $n$ of the alternating sources is

NTA AbhyasNTA Abhyas 2022

Solution:

The wire will vibrate with the same frequency as that of the source. This can be considered as an example of forced vibration.
$T=10\times 9.8\,N=98\,N$
$m=9.8\times 10^{- 3}\,kgm^{- 1}$
Frequency of wire
$n=\frac{1}{2 L}\sqrt{\left(\frac{T}{m}\right)}$
$=\frac{1}{2 \times 1}\sqrt{\left(\frac{98}{9.8 \times \left(10\right)^{- 3}}\right)}=50\,Hz$