About Frequency

As I’m sure you know, the approximate range of frequencies that us humans detect is ten octaves (doublings of frequency), from 20 Hz. to 20 kHz. Such frequencies are related to our sensory perceptions of “highness” and “lowness” of sound, and also, less directly, to our sense of pitch. When we say “frequencies,” what we really mean is “unique rates of change of density.”

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	Varying density in air over time as (approximately) a sine wave motion (from Total Recording, by permission of KIQ Productions).

Such an expression is the long way of saying “sine wave.” The waveshape known as a sine wave is a particular, very special shape describing the periodic change in density in the air over time. That shape is equivalent to seeing a spiral motion (like a spring, for instance) from the side. It represents energy vibration at a SINGLE unique frequency. All other waveshapes involve multiple frequencies. They can be reduced, through a mathematical technique called Fourier Analysis, into an array of sine waves, each having its own frequency, amplitude and phase. Whew!

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	A sine wave at 1 kHz. (from Total Recording, by permission of KIQ Productions).

This concept becomes very important when we consider low frequencies. When we go below a frequency of approximately 20 Hz., we can no longer detect that vibration of air density with out ears. So, a sine wave of 10 Hz. is inaudible. However, a square wave of 10 Hz. WILL be audible, as a series of clicks. This leads us to the insight that it is not the frequency of the wave which determines audibility, but rather the RATE OF CHANGE of air pressure.

At very high frequencies, the inertia of the ear drum limits our ability to detect sounds. The change in pressure away from average pressure and back happens for such a short period of time that the ear drum does not time to move in response.

So, the range of “unique single frequencies” we can hear is limited at low frequencies by rate of change in air pressure and at high frequencies by the inertia of our ear drum.

Nonetheless, there ARE frequencies of air density change above and below our hearing range. Frequencies at or below our low frequency limit are called infrasound or sub-audio sound. Frequencies above our hearing limits are called ultrasound.

Infrasound (low frequencies) is fascinating stuff. The stuff between 1 and 40 Hz. has some startling effects on humans. When it is at low amplitude levels, it is not audible, but at high amplitude levels it is (at least down to 20 Hz.), and it also has a related effect of becoming tactile, so that as it becomes loud enough, it can be “felt” on the skin. This tactile quality has a very powerful psychological effect on humans. In addition, there is a pharmacological effect as well, in that the presence of infrasound stimulates the human organism (that’s us, dude!) to generate adrenaline, leading to a state of heightened tension and readiness for physical activity (leading to the so-called “fight or flight” syndrome). Our evocation of these functions via the use of subwoofers is obvious and spectacularly successful!

At the same time, the volume of air required to generate significant amplitude (and loudness) changes with frequency, so that as the frequency gets lower, the amount of air needed to generate an equal amount of air density change (amplitude) goes way, way up. This is why woofers need to be big. A small driver simply cannot displace enough air to generate a meaningful pressure wave that is, say, 56 feet long (at 20 Hz.).

Below 1 Hz., we encounter the realm of atmospheric density, where the wavelengths are so long (1/5th of a mile at 1 Hz.) and the volume of air required is so great that it only occurs as a function of weather related phenomena, such as wind and barometric pressure. Interestingly, wind can be thought of as direct current, and as such it doesn’t have a frequency and we don’t hear it. What we hear is the turbulence generated by it as the wind flows by. When wind howls or whistels, that turbulence has become periodic, like in any wind instrument (now you know why they’re called “wind” instruments, eh?). Barometric pressure is the lowest frequency we encounter in air, with a period of about a week on average. We don’t hear it and we don’t feel it, although there is some indication that extreme barometric pressures and/or pressure changes do affect mood.

On the ultrasonic end of things, sound as such goes on up to about 1 megahertz in air. The limiting factor is the size of oxygen molecules. When the wavelength of the density change becomes approximately equal to or shorter than the size of the molecule itself, that wave can no longer be propagated, because the molecule is not itself compressible. That said, many mammals hear up to 100 kHz. and there is plenty of viable sonic information from musical instruments, etc. in the ultrasonic range. However, humans really DON’T seem to make much, if any, use of this information. In spite of the many rumors and speculations, stuff above 20 kHz. really does seem to be beyond us.

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