About Amplitude

Meanwhile, while the RATE of change is called “frequency,” the AMOUNT of change in density in air is called “amplitude.” It is related to our sensory perception of loudness. Now, there are limits to the amount of variation in density that air is capable of, at least for all practical purposes. For a given space at some given point in time, there are some number of molecules in that space. In the absence of displacement or motion of objects within the space, the density distribution of molecules is approximately equal everywhere in the space. This is the condition we sense as “silence,” which is equivalent to a lack of motion of air molecules and consequently no changes in density that would occur as a result of such motion.

However, the molecules never stop moving completely – there is always random motion of molecules moving about in the gaseous space, colliding with each other with random incidence and direction (this only stops completely when the temperature gets down to what is known as “absolute zero” – 460° below zero degrees Fahrenheit). This is called “thermal noise.” At normal room temperatures it is approximately an average fluctuation in density of 50-100 trillionths of an atmosphere. This is a small enough fluctuation that us humans mostly don’t hear it. It is somewhat below our “threshold of hearing” (which is approximately 200-500 trillionths of an atmosphere – 200 triillionths of an atmosphere being labeled 0 dB SPL).

What is an atmosphere? It is the average air density at the surface of the earth, at a given temperature (typically 70° F.) It is expressed in terms of the pressure of such air on the ground due to the force of gravity, and is slightly less than 15 pounds/square inch. In the metric system, it is quite elegantly expressed as “one bar.” I like it!

This leads us to the maximum amount of pressure fluctuation that can occur. For a sine wave that level occurs when 100% modulation occurs, or when the density swing is equal to the average pressure, or one atmosphere (bar). This level is approximately 195 dB SPL. At this level, the “negative density” (rarefaction part of the wave) is effectively equal to zero, or a vacuum, so above this level, the air will distort. (Actually, it begins to distort at much lower levels – some years ago I was told by an engineer doing noise reduction work on jet engines for Pratt & Whitney that air non-linearities begin around 125 dB SPL, while engineers at Bang & Olufsen tell me they have measured it at a somewhat higher level, around 160 dB SPL for 3% harmonic distortion).

There can be sounds louder than 195 dB SPL, of course. They simply can’t be sine waves. And in reality, we can consider 195 dB SPL to be an upper limit for amplitude. Just so you know, the acoustic power needed to generate such a sound is somewhare around 1 gigaWatt! In any case, this range of amplitudes is huge: 6 billion to one. Meanwhile, us humans find any amplitude greater than 2 ten-thousandths of an atmosphere (120 dB SPL) to be quite painful. We don’t go there often.

On the soft end of things, there has developed over the past century a miasma of low-level noise pollution throughout the civilized world (and, thanks to airplanes) much of the rest of the world. As a result, we simply don’t encounter “still air” very often. Mostly, the air sort of rumbles and bumbles along at an average amplitude of about 40 dB SPL, which is about 20 billionths of an atmosphere. Fortunately, such low-level turbulence and noise consists of low frequencies (less than 100 Hz.), to which us humans are less sensitive than high frequencies.