Question

A metal wire of linear mass density of $9.8g{m}^{-1}$ is stretched with a tension of $10kg-wt$ between two rigid supports $1m$ 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)

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