EECS20N: Signals and Systems


A sinusoidal sound has not just a frequency, but also a phase. The phase may be thought of as the relative starting point of the waveform. In the following applet, you can adjust the phase of up to three sinusoids and listen to the sum.
If you were able to run applets, you would have a Phase demo here.

Try first listening to the "A" signal alone, which is a 440 Hz tone, and adjusting the phase. Note that there is no audible effect. This is not surprising, since the absolute starting point of the sinusoids is obviously irrelevant. Somewhat more surprising is that when two or more sinusoids are added together, the relative phase has a significant impact on the shape of the waveform, but no impact on the perceived sound. The human ear is relatively insensitive to phase. If these waveforms represented something other than sound, like stock prices for example, the effect of phase could be quite significant.

There are certain circumstances in which the human ear is sensitive to phase. In particular, when two sinusoids of the same frequency combine, the relative phase has a big impact, since it affects the amplitude of the sum. For example, if the two sinusoids differ in phase by 180 degrees, then when they add, they exactly cancel, yielding a zero signal. Also, the human brain can use the relative phase of a sound in the two ears to help spatially locate the origin of a sound. Finally, audio systems with two speakers, which simulate spatially distributed sounds ("stereo"), can be significantly affected by the relative phase of the signal produced by the two speakers.