Do Overtones Come After the First Harmonic?

Overtones can take any value of the fundamental frequency. 1st overtone is called second harmonic and so on. Those overtones which are integral multiple of fundamental frequency are harmonics as already explained above.

Is the first overtone the second harmonic?

Another term sometimes applied to these standing waves is overtones. The second harmonic is the first overtone, the third harmonic is the second overtone, and so forth.

Is the first overtone The first harmonic?

The first overtone is the first allowed harmonic above the fundamental frequency (F₁). In the case of a system with two different ends (as in the case of a tube open at one end), the closed end is a node and the open end is an antinode. The first resonant frequency has only a quarter of a wave in the tube.