Q. A metal wire of liner mass density of $9.8\ gm^{- 1}$is stretched with a tension of 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) 50 Hz
B) 100 Hz
C) 200 Hz
D) 25 Hz
Explanation
(a) The wire will vibrate with the same frequency as that of source. This can be considered as an example of forced vibration.
T=10×9.2N=98N
$m = 9.8 \times 10^{- 3}kgm^{- 1}$
Frequency of wire
$n = \frac{1}{2L}\sqrt{\left( \frac{T}{m} \right)}$
$= \frac{1}{2 \times 1}\sqrt{\left( \frac{98}{9.8 \times 10^{- 3}} \right)} = 50Hz$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.