amadeux | If two tuning forks of slightly different pitch are struck simultaneously, the resulting sound waves and wanes periodically. The modulations are referred to as beats; their frequency is equal to the difference between the frequencies of the original tones. For example, a tuning fork with a characteristic pitch of 440 hertz, if struck at the same time, will produce beats with a frequency of six hertz.
In modern investigations tuning forks are replaced by electronic oscillators, which can supply tones of precisely controlled pitch, purity, and intensity. Beats are produced when the outputs of two oscillators tuned to slightly different frequencies are combined electrically and applied to a loudspeaker. Alternatively, the signals can be applied individually to separate speakers and the beats will still be heard. The result is the same whether the tones are combined electrically and then converted into sound, or converted into sound separately and then combined.
A quite different phenomenon results when stereophonic earphones are used and the signals are applied separately to each ear. Under the right circumstances beats can be perceived, but they are of an entirely different character. They are called binaural beats, and in many ways they are more interesting than ordinary beats, which in this discussion will be called monaural.
Monaural beats can be heard with both ears, but one ear is sufficient to perceive them. Binaural beats require the combined action of both ears. They exist as a consequence of the interaction of perceptions within the brain, and they can be used to investigate some of the brain’s processes.
The physical mechanism of monaural beats is a special case of wave interference. At any instant the amplitude of the resulting sound is equal to the algebraic sum of the amplitudes of the original tones. The signals are reinforced when they are in phase, that is, when the peaks and nulls of their waves coincide. Destructive interference diminishes the net amplitude when the waves are in opposition. The pure tones used in these experiments are described by sine waves’ the resulting beats are slowly varying functions similar to, but not precisely conforming to, a sine wave.
A beat frequency of about six hertz, as in the example given above, would sound something like vibrato in music (although vibrato is frequency modulation rather than amplitude modulation). If the interval between frequencies is made smaller, very slow beats can be produced, down to about on per second, to perceive. Rapid beats, up to about 30 hertz, are heard as roughness superimposed on the sound, rather like a Scotsman’s burr. With still greater intervals beats are not heard; the two tones are perceived separately.
Beats are rarely encountered in nature because in nature sustained pure tones are rare. They abound, however, in mechanical devices. In an airplane, jet engines operating at slightly different speeds may produce a very strong-beat, often recognized only as a feeling “in the pit of the stomach.” Acoustical engineers can filter out the whine of the engines, but the slow vibrations are difficult to suppress. Occupants of apartment houses may be annoyed by beats produced by machinery, such as two blowers running at different speeds, but they will have a hard time finding the source.
On the other hand, beats are used to advantage where frequencies must be determined precisely. Electrical engineers compare the output of a test oscillator with that of a standard oscillator by detecting the beats produced when their signals are combined. The tuning of pianos is another process that depends on beats. Typically the piano tuner will first listen for the beats produced by a tuning fork of 440 hertz and the A above middle C, and tighten or loosen the A wire until the beats slow to zero. He then strikes the A key and the D key below it and tunes the latter wire until 10 beats per second are heard. That frequency is produced by the interaction of the A string’s second harmonic, or second multiple (2 x 44 0 = 180), and the D string’s third harmonic (3 x 290 = 870). In this fashion, key by key, the piano is tuned; in theory it could be done even by someone who is tone-deaf.
Binaural beats were discovered in 1839 by a German experimenter named H. W. Dove, but as late as 1915 they were considered a trivial special case of monaural beats. It was argued that each ear was hearing sounds intended for the other. This extraneous result could be eliminated by placing the tuning forks in separate rooms, with the subject in a third room between them, and guiding the sounds through tubes to each ear. It was necessary to carefully seal each tube to the head, however, and another objection was raised; that sound presentation to one ear could be conducted through the skull to the other.
Bone conduction is well established, and indeed some hearing aids operate on this principle, although sound is attenuated a thousandfold from ear to ear. The possible contribution of bone conduction to the perception of binaural beats is eliminated, however, by the use of modern stereophonic earphones. Such earphones have padding, often liquid filled, to insulate the head from the sound source, and are designed explicitly to prevent conduction effects. Indeed, stereophonic recordings played through earphones can sound unnatural because the instruments seem too isolated.
The difference most immediately apparent between monaural and binaural beats is that binaural beats can be heard only when the tones used to produce them are of low pitch. Binaural beats are best perceived when the carrier frequency is about 440 hertz; above that frequency they become less distinct and above about 1,000 hertz they vanish altogether. No person I have tested reports hearing beats for frequencies above 900 hertz. Experimental conditions, particularly the intensity of the sounds and the type of earphones used can affect the results, however, and other investigators report detecting beats produced by tones up to almost 1,500 hertz. At the other end of the scale beats also become elusive. Below about 90 hertz the subject may confuse the beats with the tones used to produce them.
J. C. R. Licklider of the Massachusetts Institute of Technology developed a technique when he was working at Harvard University to measure a spectrum of binaural beats [see upper illustration on page 102]. He adopted the frequency of one oscillator until the interval was large enough so that the beats seemed “rough”; then he noted the frequency of the unchanged reference oscillator. Next he changed the setting of the reference oscillator and repeated the procedure. In this way the range of perception of each subject was recorded.
Another distinguishing characteristic of binaural beats is their muffled sound. Monaural beats produced with sounds of equal intensity pulse from loudness to silence, as their wave form would suggest. Binaural beats, on the other hand, are only a slight modulation of a loud background. I have tried to estimate the depth of the modulation, and it seems to be about three decibels, or about a tenth of the loudness of a whisper. In order to help subjects recognize these relatively faint effects I usually present signals with monaural beats and then suddenly change to the binaural mode. With tones of about 440 hertz it usually takes two or three seconds for the subject to recognize the binaural beats.
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