Question

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

• A. $50Hz$
• B. $100Hz$
• C. $200Hz$
• D. $25Hz$

Answer 1

Answer: (A)

$50Hz$

Answer 2

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