Our senses, especially our eyes and ears, are remarkably precise instruments. We can distinguish the slightest gradations in intensity, color, frequency, etc. Nonetheless, eyes and ears are also easily fooled.
For instance, in well known optical experiments straight lines may look bent or equally long lines seem to have different lengths These experiments tell us, that the brain processes involved in perception also play an important role in the way we see and hear our world.
The study of the physiological and mental processes of hearing is called psychoacoustics. Principles of psychoacoustics are widely used in audio technology. An example of psychoacoustic processing is data compression with MPEG-3, which removes information from the signal without (or almost without) affecting sound quality. Another example is the loudness button on many amplifiers that compensates for the reduced sensitivity of the ear for the highest and lowest frequencies at low sound pressures.
In this article a device is presented that makes signals below 60 Hz audible in loudspeakers and headphones that normally, by their mere physical construction, are not able to reproduce these frequencies. The device combines two psychoacoustic phenomena.
The principle of the missing fundamental:
The sound of a single note of a music instrument is the summation of its fundamental tone (say 200 Hz) and a number of harmonics (400, 600, 800, 1000, …. Hz). If we electronically remove the 200 Hz fundamental tone our ear only hears the harmonic frequencies at 400 Hz and higher. Nonetheless our brain tells us that the pitch of the note is 200 Hz. Since the 600 and 1000 Hz frequency components are no fundamentals of the lowest (400 Hz) frequency component present, our brain knows that something is missing and “adds” an imaginary fundamental tone of 200 Hz. However, the “color” of the note is lighter when the fundamental tone is missing.
Mechanical harmonic distortion in the inner ear:
A pure 200 Hz sine wave not only makes the basillary membrane inside the ear vibrate at 200 Hz, but also at 400, 600, 800, 1000, 1200…. Hz. For sine waves between 200 and 3000 Hz these overtones have amplitudes of 33%, 13%, 6%, 4%, 2%, …. of the amplitude of the fundamental. Harmonic distortion in the inner-ear thus sums up to approximately 60%!
Nonetheless, we only hear a pure sine-wave at the fundamental frequency since our brain has learned that this specific frequency spectrum belongs to a pure tone.
To my knowledge, nobody has ever investigated the frequency spectrum of the basillary membrane at very low frequencies. However, the decreasing sensitivity of the ear indicates that the membrane is relatively “stiff” for this frequency range. Therefore it can be expected that the relative amount of overtones at the lowest frequencies strongly increases. This phenomenon is seen with many music instruments. A “cheap” piano does not really produce a 27.5 Hz tone when one strikes the lowest key, because the resonance board is simply too small to swing at 27.5 Hz, but it produces a tone that appears to be 27.5Hz due to the principle of the missing fundamental.
At their lowest frequencies corpses are more ready to vibrate at the overtones than at the fundamental. My guess was that in the inner ear the information on the lowest tones thus will be merely transmitted by the overtones produced.
Most loudspeakers and headphones are not able to make the air move at frequencies between 20 and 50 Hz and therefore these frequencies will not be heard. However, if we electronically create harmonics of these lowest tones and add these signals to the original audio-signal, we suddenly will hear the low fundamentals, due to the principal of the missing fundamental. Moreover, my speculation was, that if the spectrum of these overtones was chosen so as to create an energy spectrum on the basillary membrane that, except for the fundamental tone, resembles that of a pure sine wave, then we will hear something that is very close to this sine tone.
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