Synthesis of a Complex Wave in Terms of Harmonics

Consider, first, the second harmonic with frequency / 2 = 2/1• Figure V .17 shows one period of it, somewhat enlarged to make the details clearer,

PART V. DESCRIPTIVE PHYSICS OF COMPLEX SOUNDS 177

Without giving a proof, it turns out that by superimposing all of the odd harmonics with the nth-harmonic having peak pressure Pin yields the square wave. So, formally, the recipe is:

3.1.2 Sawtooth Wave. Consider a wave of the sawtooth form shown in Fig. V.20. The spectrum in this case turns out to be every harmonic n in the amount Pin, which is plotted in Fig. V.21.