22 Chapter 1
time, the output waveform must be the sum of all the sounds. An ideal microphone
connected by ideal amplifi cation to an ideal loudspeaker will reproduce all of the sounds
simultaneously by linear superimposition. However, should there be a lack of linearity
anywhere in the system, the sounds will no longer have an independent existence, but will
interfere with one another, changing one another’s timbre and even creating new sounds
that did not previously exist. This is known as intermodulation. Figure 1.17 shows that a
linear system will pass two sine waves without interference. If there is any nonlinearity,
the two sine waves will intermodulate to produce sum and difference frequencies, which
are easily observed in the otherwise pure spectrum.
1.10 The Sine Wave .........................................................................................................
As the sine wave is such a useful concept it will be treated here in detail. Figure 1.18
shows a constant speed rotation viewed along the axis so that the motion is circular.
Imagine, however, the view from one side in the plane of the rotation. From a distance,
only a vertical oscillation will be observed and if the position is plotted against time the
resultant waveform will be a sine wave. Geometrically, it is possible to calculate the
height or displacement because it is the radius multiplied by the sine of the phase angle.
Figure 1.17 : (a) A perfectly linear system will pass a number of superimposed waveforms
without interference so that the output spectrum does not change. (b) A nonlinear system
causes intermodulation where the output spectrum contains sum and difference frequencies
in addition to the originals.