Q18 of 36 Page 109

A Sonometer wire is vibrating in resonance with a tuning fork. Keeping the tension applied same; the length of the wire is doubled. Under what conditions would the tuning fork still be in resonance with the wire?

When wire of length L is made to vibrate, its resonance frequency in nth mode after stretching it by tension T, then Frequency

[Here, m= mass per unit length of stretched wire]


The two given cases are:


---------------------- (i)


---------------------- (ii)


According to question;


(Mass of wire m is same in both cases)



Equation (i) divided by Equation (ii);



Since, the turning forks in the both cases are also same.


.


.


Hence, when the length of wire is doubled, the number of harmonic wave also doubles for same resonant frequency.


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