An audio compact disc (CD) holds up to 74 minutes, 33 seconds of music, just enough for a complete recording of Ludwig van Beethoven’s Ninth Symphony on one disc. Each second of music is stored as a string of about 1.5 million bits, represented as tiny, narrow pits on the disc’s surface. These pits range from 0.9 to 3.3 micrometers in length and correspond to the 1s and 0s of the digital signal encoding the sound. It takes more than 6 billion bits, recorded on a spiral track several kilometers long but only 0.5 micrometer wide, to capture the entire symphony.
Mathematical elements make significant contributions to the crisp digital sound delivered by an audio CD. Sampling theory, for instance, guides how often sound waves should be measured to generate a digital signal that adequately reproduces the original sound.