Question

A metal wire of linear mass density of 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 n. The frequency n of the alternating source is

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

Answer 1

Answer: (A)

50 Hz

Answer 2

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