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 is resonance with the wire?

A sonometer wire is vibrating in resonance with a tuning fork. Keeping

1.	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 is resonance with the wire?
Answer» Solution :INITIALLY `f _(1) = (1)/( 2L ) sqrt ((T)/(mu)) = f ` (FREQUENCY of given tuning fork) Finally, `f ._(1) = (1)/(2 (2 L )) sqrt((T)/(mu))` `(because ` Length of wire is made doubled) For SECOND harmonic of sonometer wire, `2 f._(1) = 2 xx (1)/(2 (2L)) sqrt ((T)/( mu ))` `= (1)/( 2 L ) sqrt ((T)/( mu))= f` Thus, given tuning form will resonate with given sonometer. (i) initially in first harmonic (i.e. fundamental frequency). (II) finally (when length of wire is doubled in second harmonic (i.e. first overtone)