Science and Math for Audio Humans – Sound Itself

by Danny Maland

First off, here's my standard disclaimer for this series: Everything that I set before you should be read with the idea that “this is how I've come to understand it.” If somebody catches something that's just flat-out wrong, or if you just think that an idea is debatable, please take the time to start a discussion via the comments.

Audio folks spend vast amounts of time dealing with actual sound in the actual world. That is to say, sonic events that are happening in the air, as opposed to signals that ultimately correspond to sonic events. This being the case, an understanding of what sounds really are, and how they behave, can be a very handy thing to have in the ol' mental toolkit.

Sound is a fairly basic sort of animal, when you get down to it. Any sound pressure wave that you encounter is air molecules being pushed together (compression) and expanding apart (rarefaction) at regular intervals. The pressure wave attempts to travel outward from its source equally in all directions, creating a spherical pattern of radiation. The caveat with this, though, is that truly spherical sound radiation is rarely observed. The source of the sound has to be small, relative to you, and there can be no obstructions for the pressure wave to encounter.

To get into this a bit, the ideal definition of “small” is that of a geometric point, which occupies no space whatsoever. While you can get far enough away from a sound source for it to act like a geometric point – that is, far enough away that the difference in distance from you to any place on the source is negligible – it's rather more difficult to get rid of all obstructions. A small loudspeaker that's several hundred feet away from you, sitting in an empty field, is still sitting on a giant obstruction. That obstruction being the ground.

You can use Figure 1 to help you visualize all this. The top frame shows a sound source in a 2-dimensional world, with a pressure wave radiating out equally in all directions. The middle panel shows radiation in the horizontal and vertical planes, to help show how a sphere would be created if you had an infinite number of intermediate planes. The last panel illustrates the “source sitting in a field” idea, with the ground obstructing the downward radiation of the pressure wave.

  • Quite a lot of people represent sound as traveling like “ripples on a pond.” While this is partially true, especially when trying to get an idea of a sound's overall radiation pattern, the analogy omits an interesting detail. Water ripples are what you would call a “transverse” wave. If you look up the meaning of “transverse,” what you get is that the word is an adjective meaning that something is across something else. Transverse waves move between two states (oscillate) in a direction perpendicular to their vector of travel. If a transverse wave is propagating, or moving outward from an origin, in a horizontal direction, then the “swing” of the oscillation is in the vertical direction. By contrast, sound pressure waves in air are a longitudinal wave. The oscillation of a longitudinal wave is parallel to the propagation vector. If a sound pressure wave is heading north from Salt Lake City, its oscillation will be to the north and south.
  • Figure 2 is a visual example of the difference between transverse and longitudinal waves. The top panel depicts two cycles of a transverse wave, and the bottom panel is two cycles of a longitudinal wave.

Even with the reality of sound pressure waves being longitudinal when in air, later diagrams will depict sound pressure waves as though they were transverse. The reason for this is convenience. It's rather easier to create complex diagrams of transverse waves than their longitudinal counterparts, mostly because (in my opinion), the separation of visual information into two axes makes for clearer pictures. The visual information gets more spread out, and becomes easier to take in.

If you were to ask me, I would tell you that I rarely think about the topics presented above – at least, not directly. However, the reason to include this material in the series is that it provides a foundation for the rest of what we'll talk about in relation to sound pressure wave characteristics. In turn, that material is foundational to discussions that happen down the road. The “basement level” topics that don't cross your mind that much in working reality retain their importance because of their relationship to all the things that DO cross your mind in everyday life.

Well, at least in everyday audio life.