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I've heard that digital encoding on audio CDs represents a pressure wave. But audio has so many components like volume, pitch, and timbre; how can the binary encoding of a pressure wave encompass all these attributes? RY, Madison Wisconsin.

cdThe binary encoding on a CD provides the CD player with a series of 16-bit numbers. Written in decimal notation, those numbers can range from 32,768 to -32,767. Each number represents an air pressure measurement made near the microphone during the recording process. The negative numbers correspond to dips in the local air pressure while the positive numbers reflect rises in pressure. The CD player uses speakers to reproduce those pressure fluctuations and with them, the sound waves that reached the microphone long ago. But you're wondering how these numbers can represent features as subtle as volume, pitch, and timbre.

The answer lies in the structure of the pressure fluctuations that are faithfully represented by those numbers. All the nuances of sound and music are contained in the pressure fluctuations themselves. Volume is reflected by the amplitudes—the larger the fluctuations, the greater the volume. Pitch is set by the frequency—the faster the pressure flips from above normal to below normal and back again, the higher the sound's pitch. And timbre is established by the detailed structure of each pressure wave: a flute produces smoothly varying, almost sinusoidal pressure fluctuations while a trumpet's pressure fluctuations are complicated and highly structured.

At a deeper level, timbre and pitch are interrelated because pressure fluctuations that are more complicated than a simple sinusoidal pattern actually contain more than a single pitch. These additional pitches are called overtones and, in some cases, harmonics of the fundamental pitch involved. By measuring, recording, and reproducing all of the details in the pressure fluctuations at a microphone, audio systems accurately reproduce sound, music, and voice. The fact that those measurements are recorded using a series of 16-bit binary numbers makes little difference in the final result, except that it ensures that relatively high quality sound emerges from the speakers.

Answered by Louis A. Bloomfield of the University of Virginia