Audio Principles 19Microphones have no such ability, which is why acoustic treatment is often needed in
areas where microphones are used.
A further example of the fi nite time discrimination of the ear is the fact that short
interruptions to a continuous tone are diffi cult to detect. Finite time resolution means that
masking can take place even when the masking tone begins after and ceases before the
masked sound. This is referred to as forward and backward masking.^6
Figure 1.14(a) shows an electrical signal in which two equal sine waves of nearly the
same frequency have been added together linearly. Note that the envelope of the signal
varies as the two waves move in and out of phase. Clearly the frequency transform
calculated to infi nite accuracy is that shown at Figure 1.14(b). The two amplitudes are
constant and there is no evidence of envelope modulation. However, such a measurement
requires an infi nite time. When a shorter time is available, the frequency discrimination of
the transform falls and the bands in which energy is detected become broader.
Figure 1.14 : (a) Result of adding two sine waves of similar frequency. (b) Spectrum of (a)
to infi nite accuracy. (c) With fi nite accuracy, only a single frequency is distinguished whose
amplitude changes with the envelope of (a) giving rise to beats.