## 1 Introduction
According to the Fourier transform, a waveform in the time domain is a superposition of a series of sinusoidal waveforms and can be described by a mathematical formula, as shown in Equation (1):  
\[\mathrm{f}(\mathrm{t})=\mathrm{A_{1}}\ \sin(2\pi\mathrm{f_{1}}\mathrm{t}+ \phi_{1})+\mathrm{A_{2}}\ \mathrm{sin}(2\pi\mathrm{f_{2}}\mathrm{t}+\phi_{2})+\mathrm{A_{3}}\ \mathrm{sin}(2\pi\mathrm{f_{3}}\mathrm{t}+\phi_{3})+\dots \tag{1}\]  
where \(\mathrm{A_{1}}\) is the amplitude, \(\mathrm{f_{1}}\) is the frequency of the fundamental waveform, and \(\varphi_{1}\) is the initial phase of this waveform (it was equal to \(0^{\circ}\)). The frequencies of the other components are integer multiples of the frequency of the fundamental wave. If the signal is periodic with a given frequency \(\mathrm{f_{1}}\), the other frequencies that make up the signal are integer multiples of this frequency, i.e., \(\mathrm{f_{1}}\), \(\mathrm{f_{2}}\mathrm{f_{1}}\), etc. ; they are all integral multiples of the fundamental frequency. Thus, in the case of even multiples, these will be \(2\mathrm{f_{1}}\), \(4\mathrm{f_{1}}\), \(6\mathrm{f_{1}}\), \(8\mathrm{f_{1}}\), \(10\mathrm{f_{1}}\), etc. These frequencies are called harmonics, just like the first harmonic (\(\mathrm{f_{1}}\)), i.e., the fundamental frequency. For example, if the fundamental frequency is equal to 20 Hz (also known as the first harmonic), the second harmonic will be 40 Hz (20 multiplied by 2 equals 40), the fourth harmonic will be 80 Hz, etc. From a practical point of view, even harmonics relating to the order components, which can be obtained by Fourier series decomposition, will be used for this. In electrical engineering, even harmonics occur with large load spikes or errors in converters (such harmonics can be of any amplitude and typically become smaller as frequency increases), but for the purposes of the experiment, they were generated in a generator. In practice, in addition to even harmonics, there are also odd harmonics, but these higher harmonics were omitted from the analysis due to the study of the effect of even harmonics on flame extinguishing using low-frequency acoustic waves. In summary, many solutions are known to both indirectly and directly extinguish and control flames with the use of acoustic waves generated in the sound source. However, considering the scientific literature, apart from the work of the author and his co-authors, and a few other works (most of them are included in the bibliography of this paper), there is a noticeable lack of publications on the use of acoustic waves generated from a sound source with high and very high acoustic power for extinguishing and controlling flames. The experiments conducted so far have found that both modulated (of different shapes) and unmodulated acoustic waves can be applied to extinguish flames, which is a scientific novelty. The analysis of the extinguishing capabilities of acoustic waves, particularly using low-frequency waves with harmonics, allows one to fill the gap in the literature in this area. This may, in the long run, contribute to a better understanding of acoustic methods, including the limits of the use of this technique, which becomes possible through the selection of appropriate parameters of the acoustic signal (in particular, the frequency and shape of the waveform, the type of modulation, and as presented in this paper--the order of harmonics). In this sense, the experimental research showed that it may contribute to a better understanding and discovery of the regularities that occur, in order to benefit in the future from the possibility of using low-frequency acoustic waves generated by a sound source with high and very high acoustic power to extinguish flames.