Illusions, Riddles, & Toys

Remember the old mathematical riddle about moving a football from a hundred yards out to the goal line? Known as Xeno's Paradox, it goes like this: if each time the ball is moved it travels half the distance to the goal, how many moves will it take to get there? The answer: an infinite number, because no matter how many times you cut the distance to the goal by half, you'll always be some infinitesimal distance away from it.

We audiofools face just such a riddle in our relentless pursuit of musical realism. I can hear you now: No, say it isn't so. Surely our technology is equal to the task. I'm sorry to tell you that it isn't, and probably never will be. One good reason: a couple of pesky laws of physics governing the behavior of transducers. Transducers, for those of you who weren't in class the day we covered them, are devices that convert one form of energy into another. Microphones, which convert airborne soundwaves into electrical signals, and loudspeakers, which do the opposite, are two related varieties of a class of such devices called electroacoustical transducers.

The business end of a microphone contains a lightweight element that moves in response to instantaneous changes in local air pressure---the back-and-forth motions of soundwaves called compression and rarefaction. As the element moves, it induces an analogous electrical signal in the wires to which it is attached. (In the real world, analogous means similar to, not exactly like.) This signal is recorded onto a storage medium for later playback. During playback (the part of the cycle that so greatly fascinates audiophiles), the signal is amplified to sufficient strength to set a loudspeaker in motion, thereby moving air that reaches our ears in the form of, we hope, enjoyable music.

Believe it or not, the signal produced by the microphone actually remains pretty well intact as long as it's confined to the electronic realm, analog or digital. Despite all the research into all the various forms of distortion that can alter an electrical waveform, and the supertanker's worth of ink that has been spilled in discussing them, relatively little light has been shed on the fact that most of the damage done to the integrity of the musical signal happens at the air/transducer interface---probably because there's not much we can do about it.

Bodies at rest, bodies in motion
Isaac Newton, who spent a lot of time observing and thinking about the things around him, came up with a simple, elegant explanation for their behavior: Bodies at rest tend to remain at rest, and bodies in motion tend to remain in motion.

A microphone element in a quiet room is a body at rest. It resists moving until changing air pressure overcomes its inertia and sets it in motion. Now it has become a body in motion and will resist moving in the opposite direction, which it must to accurately transcribe the soundwaves acting upon it. At each change of direction there is a brief but unavoidable delay.

(If you've ever had to push a stalled car, you've experienced such a delay: You push against the car. At first, nothing seems to be happening. Your leg muscles contract, but the car remains where it is. Force is being applied, but the energy of the applied force is being absorbed by the inertia of the car's weight and mass. You get mad, push a little harder, and Wow! the car moves. You know that once you've got it moving it's easier to keep it moving than it is to stop and rest and have to start all over again.)

The microphone element in motion is moving at more or less the same rate as the soundwaves making it move; it is an oscillating body, and oscillating bodies exhibit a peculiar form of behavior known as resonance, which means that they favor some frequencies over others. The net effect of these two mechanical phenomena, delayed response and resonance (for the sake of simplicity I'm ignoring a host of electrical effects governing the behaviors of transducers), result in the characteristic deviation from accuracy we call a coloration. All microphones and all loudspeakers have audible colorations, and are therefore inaccurate. Always have been, always will be. And loudspeakers? They also have a host of other problems, meaning that a loudspeaker will never be able to launch a violin's waveform into a room the way a violin can. This fact alone ensures that we will never get all the way to the goal of a truly realistic reproduction of sound.