Audio Principles 23The phase angle is obtained by multiplying the angular velocity ω by the time t. Note that
the angular velocity is measured in radians per second, whereas frequency f is measured
in rotations per second or hertz. As a radian is unit distance at unit radius (about 57°),
then there are 2 π radians in one rotation. Thus the phase angle at a time t is given by
sinωt or sin2 πft.
A second viewer, who is at right angles to the fi rst viewer, will observe the same waveform
but with different timing. The displacement will be given by the radius multiplied by the
cosine of the phase angle. When plotted on the same graph, the two waveforms are phase
shifted with respect to one another. In this case the phase shift is 90° and the two waveforms
are said to bein quadrature. Incidentally, the motions on each side of a steam locomotive
are in quadrature so that it can always get started (the term used is quartering). Note that the
phase angle of a signal is constantly changing with time, whereas the phase shift between
two signals can be constant. It is important that these two are not confused.
Figure 1.18 : A sine wave is one component of a rotation. When a rotation is viewed from
two places at places at right angles, one will see a sine wave and the other will see a cosine
wave. The constant phase shift between sine and cosine is 90° and should not be confused
with the time variant phase angle due to the rotation.