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I was using a sonometer to verify the frequency of a.c. supply in the lab is 50 Hz. For this the equation I used is f=(1/4L) x Sq. root (T/m) I set tension T = 4.9 N by hanging 0.5kg mass mass per unit length, m of the sonometer wire was 1.8 x10^-3 kg/m.The wire was magnetic and was put under the influence of an electromagnet to which the a.c. supply was fed ( after stepping down)

When I started to separate the wedges from each other from the middle position I got the first resonance length, L as 13cm . At this condition the wire started to vibrate but the amplitude of vibration was not large . This resonance length gave me the frequency of a.c. as 100Hz but as answer should have been close to 50Hz so I moved the wedges further from each other and at separation of 26cm the again the wire started to vibration but this time the amplitude of vibration was really high. When I used this value the frequency obtained was 50 Hz. Now I wonder what was that intermediate weak resonance condition? Even though I repeated this experiment several times but the weak resonance condition was seen every time.

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Could it be that your voltage source produces harmonics of the fundamental frequency of $50\,\rm Hz$?
Did you try and find other (very small) resonances for lengths around $26/3\,\rm cm$ and $26/4\,\rm cm$?.

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  • $\begingroup$ I put both the wedges in contact beneath the potentiometer wire at the centre and started to separate bothe from each other . Only once it was seen to show resonance of small amplitude then at separation of 26 the oscillations were of large amplitude (nearly 2 cm) producing good audible sound too $\endgroup$
    – Shinnaaan
    Commented Dec 10, 2023 at 16:51
  • $\begingroup$ You can also "feel" the small resonance positions by touching the wire at the end. $\endgroup$
    – Farcher
    Commented Dec 10, 2023 at 22:43

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