Page 34 - Master Handbook of Acoustics

FIGURE 1-10 Illustration of the phase relationships between waveforms with the same amplitude
and frequency. A rotation of 360° is analogous to one complete sine-wave cycle.

In Fig. 1-9, all three components of the complex waveform of Fig. 1-9E are in phase. That is, the f 1
fundamental, the f second harmonic, and the f3 third harmonic all start at zero at the same time. What
2
happens if the harmonics are out of phase with the fundamental? Figure 1-11 illustrates this case. The
second harmonic f is now advanced 90°, and the third harmonic f3 is retarded 90°. By combining f ,
2
1
f , and f3 for each instant of time, with due regard to positive and negative signs, the contorted
2
waveform of Fig. 1-11E is obtained.