Digital Sound & Music: Concepts, Applications, & Science, Chapter 4, last updated 6/25/2013

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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.