If \( v \) is the frequency of ac mains, then the frequency of sonometer wire at resonance is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 2v \)
At resonance the wire vibrates with the frequency of the periodic force that drives it. In the usual sonometer arrangement the steel wire lies close to the poles of an electromagnet fed by the a.c. mains.
The a.c. makes the poles of the magnet reverse in every half cycle, but a magnet attracts iron whichever way its poles point. So the wire is pulled once in each half cycle, that is twice in every cycle of the mains.
\( \displaystyle T_{\text{force}} = \frac{1}{2}\times\frac{1}{v} \Rightarrow f_{\text{wire}} = 2v \)