Chapter One: An Acoustics Primer

9. What is phase?

Phase denotes a particular point in the cycle of a waveform, expressed as an angular measurement in degrees or radians. It is generally an inaudible characteristic of a single wave (although it may be perceptible when utilizing very low-frequency waves as controls in synthesis). Phase is a critical factor in the interaction of one wave with another, either acoustically or electronically.

The video example below illustrates the generation of a sine wave by plotting the vertical displacement of a spoke tip (representing the radius) of a rotating wheel (y-axis) against time (x-axis). The height of the spoke-tip corresponds to the waveform's relative amplitude, here plotted between a normalized range of +1 to −1. To measure the phase angle in degrees, we start with the initial reference of a spoke oriented horizontally to the right and designate this position as as 0º, with a relative amplitude of zero. As the wheel rotates counterclockwise, the sine wave reaches its peak positive amplitude when the spoke has traveled 90º from its starting point [Instruction: Click the image to start or stop the animation], with a relative amplitude of +1. At 180º from the starting point, the amplitude of the sine wave has returned to zero . At 270º, the sine wave reaches its peak negative amplitude of -1 and then returns to zero as it completes the full cycle at 360° (equivalent to 0°). As demonstrated on the frequency page, phase angle can also be measured in radians, with 2π radians being the equivalent of 360º, a full cycle or rotation of the wheel.

Another common sinusoidal waveform used in synthesis or measurement is the cosine wave, which is identical in shape to a sine wave and is aurally indistinguishable when presented in isolation, but is distinguished by the fact that its cycle begins 90° out of phase relative to a sine wave, or at +1.