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

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Figure 4.27 Two loudspeakers arriving at a listener one millisecond apart

Let’s assume, for the sake of simplicity, that both loudspeakers are generating a 500 Hz

sine wave, and the speed of sound is 1000 ft/s. (As stated in Section 1.1.1, the speed of sound in

air varies depending upon temperature and air pressure so you don’t always get a perfect 1130

ft/s.) Recall that wavelength equals velocity multiplied by period ( ). Then with this

speed of sound, a 500 Hz sine wave has a wavelength of two feet.

( * ( *

At a speed of 1000 ft/s, sound travels one foot each millisecond, which implies that with a one

millisecond delay, a sound wave is delayed by one foot. For 500 Hz, this is half the frequency's

wavelength. If you remember from Chapter 2, half a wavelength is the same thing as a

180o

phase offset. In sum, a one millisecond delay between Loudspeaker A and Loudspeaker B

results in a 180

o

phase difference between the two 500 Hz sine waves. In a free-field

environment with your head stationary, this results in a cancellation of the 500 Hz frequency

when the two sine waves arrive at your ear. This phase relationship is illustrated in Figure 4.28.

Figure 4.28 Phase relationship between two 500 Hz sine waves one millisecond apart

10ms 11ms