A Sonometer 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.