Digital Sound & Music: Concepts, Applications, & Science, Chapter 4, last updated 6/25/2013
42
Figure 4.29 Phase relationship between two 1000 Hz sine waves one millisecond apart
If we switch the frequency to 1000 Hz, we’re now dealing with a wavelength of one foot.
An analysis similar to the one above shows that the one millisecond delay results in a
360o
phase
difference between the two sounds. For sine waves, two sounds combining at a
360o
phase
difference behave the same as a
0o
phase difference. For all intents and purposes, these two
sounds are coherent, which means when they combine at your ear, they reinforce each other,
which is perceived as an increase in amplitude. In other words, the totally in-phase frequencies
get louder. This phase relationship is illustrated in Figure 4.29.
Simple sine waves serve as convenient examples for how sound works, but they are
rarely encountered in practice. Almost all sounds you hear are complex sounds made up of
multiple frequencies. Continuing our example of the one millisecond offset between two
loudspeakers, consider the implications of sending two identical sine wave sweeps through two
loudspeakers. A sine wave sweep contains all frequencies in the audible spectrum. When those
two identical complex sounds arrive at your ear one millisecond apart, each of the matching pairs
of frequency components combines at a different phase relationship. Some frequencies combine
with a phase relationship that is a multiple of 180
o,
causing cancellations. Some frequencies
combine with a phase relationship that is a multiple of 360
o,
causing reinforcements. All the
other frequencies combine in phase relationships that vary between multiples of 0
o
and 360
o,
resulting in amplitude changes somewhere between complete cancellation and perfect
reinforcement. This phenomenon is called comb filtering, which can be defined as a regularly
repeating pattern of frequencies being attenuated or boosted as you move through the frequency
spectrum. (See Figure 4.32.)
To understand comb filtering, let’s look at how we detect and analyze it in an acoustic
space. First, consider what the frequency response of the sine wave sweep would look like if we
measured it coming from one loudspeaker that is 10 feet away from the listener. This is the
black line in Figure 4.30. As you can see, the line in the audible spectrum (20 to 20,000 Hz) is
relatively flat, indicating that all frequencies are present, at an amplitude level just over 100
dBSPL. The gray line shows the frequency response for an identical sine sweep, but measured at
a distance of 11 feet from the one loudspeaker. This frequency response is a little bumpier than
the first. Neither frequency response is perfectly because environmental conditions affect the
sound as it passes through the air. Keep in mind that these two frequency responses, represented
by the black and gray lines on the graph, were measured at different times, each from a single
loudspeaker, and at distances from the loudspeaker that varied by one foot the equivalent of
offsetting them by one millisecond. Since the two sounds happened at different moments in
time, there is of course no comb filtering.
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