Page 33 - Master Handbook of Acoustics

that is twice the frequency (f ) of Fig. 1-9B is called the second harmonic, and the sine wave that is
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three times the frequency (f3) of Fig. 1-9D is the third harmonic. The fourth harmonic and the fifth

harmonic are four and five times the frequency of the fundamental, and so on.

Phase

In Fig. 1-9, all three components, f , f , and f3, start together at the same time. This is called an in-
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1
phase condition. In some cases, the time relationships between harmonics or between harmonics and
the fundamental are quite different from this. We observed that one revolution (360°) of the crankshaft
of an automobile engine was equated with one cycle of simple harmonic motion of the piston. The up-
and-down travel of the piston spread out in time traces a sine wave such as that in Fig. 1-10. One
complete sine-wave cycle represents 360° of rotation. If another sine wave of identical frequency is
delayed 90°, its time relationship to the first one is a quarter wave late (time increasing to the right).
A half-wave delay would be 180°, and so on. For the 360° delay, the waveform at the bottom of Fig.

1-10 synchronizes with the top one, reaching positive peaks and negative peaks simultaneously and
producing the in-phase condition.