![]() Taking the reciprocal of the beat period yields the beat frequency. Experimentally, we can determine the beat frequency by timing how long it takes for the sound to get loud N times and then dividing that time by N (where N is an arbitrary integer chosen by the experimenter-the bigger the N the more precise the result). The frequency with which the loudness pattern repeats itself is called the beat frequency. To a person whose ear is at a location at which waves from both sources exist, the sound gets loud, soft, loud, soft, etc. Then the trough from the lower-frequency source starts “falling behind” until, eventually a crest from the higher-frequency source is interfering with the crest preceding the corresponding crest from the lower-frequency source and the interference is again as constructive as possible. If your ear were at the point in question, you would find the sound to be inaudible or of very low volume. At that instant in time, the interference is as destructive as it gets. Eventually, a crest from the higher-frequency source is arriving at the point in question at the same time as a trough from the lower-frequency source. ![]() When the third crest from the higher-frequency source arrives, the corresponding crest from the lower-frequency source is even farther behind. The interference is still constructive but not to the degree that it was. Rather than a crest interfering with a crest, we have a crest interfering with an intermediate-displacement part of the wave. One period after the instant just discussed, the next crest (call it the second crest) from the higher-frequency source is at the point in question, but the peak of the next crest from the lower-frequency source is not there yet. ![]() Let’s mark the passage of time by means of the shorter period, the period of the higher-frequency waves. If your ear were at that location, you would find the sound relatively loud. At that instant the waves are interfering constructively, resulting in a large total amplitude. Let’s start at an instant when two sound wave crests are arriving at that point, one from each source. Consider the displacements at a particular point in space. Suppose the two frequencies do not differ by much. This amplitude will vary because the interference will alternate between constructive interference and destructive interference. The amplitude of the sound at any position in space will be the amplitude of the sum of the displacements of the two waves at that point. Any point in the air-filled region of space around the sources will receive sound waves from both the sources. \)Ĭonsider two sound sources, in the vicinity of each other, each producing sound waves at its own single frequency.
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