Digital Sound & Music: Concepts, Applications, & Science, Chapter 4, last updated 6/25/2013
Figure 4.30 Frequency response of two sound sources 1 millisecond apart
The situation is difference when the sound waves are played at the same time through the
two loudspeakers not equidistant from the listener, the frequency components arrive at the
listener in different phases. Figure 4.31 is a graph of frequency vs. phase for this situation. You
can understand the graph in this way: For each frequency on the x-axis, consider a pair of
frequency components of the sound being analyzed, the first belonging to the sound coming from
the closer speaker and the second belonging to the sound coming from the farther speaker. The
graph shows that degree to which these pairs of frequency components are out-of-phase, which
ranges between
Figure 4.31 Phase relationship per frequency for two sound sources one millisecond apart
Figure 4.32 shows the resulting frequency response when these two sounds are combined.
Notice that the frequencies that have a
relationship are now louder, at approximately 110 dB.
On the other hand, frequencies that are out-of-phase are now substantially quieter, some by as
much as 50 dB depending on the extent of the phase offset. You can see in the graph why the
effect is called comb filtering. The scalloped effect in the graph is how comb filtering appears in
frequency response graphs a regularly repeated pattern of frequencies being attenuated or
boosted as you more through the frequency spectrum.
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