24 Chapter 1
The velocity of a moving component is often more important in audio than the
displacement. The vertical component of velocity is obtained by differentiating the
displacement. As the displacement is a sine wave, the velocity will be a cosine wave whose
amplitude is proportional to frequency. In other words, the displacement and velocity
are in quadrature with the velocity lagging. This is consistent with the velocity reaching
a minimum as the displacement reaches a maximum and vice versa. Figure 1.19 shows
displacement, velocity, and acceleration waveforms of a body executing simple harmonic
motion (SHM). Note that the acceleration and the displacement are always antiphase.
Figure 1.19 : The displacement, velocity, and acceleration of a body executing simple
harmonic motion (SHM).