Answer:
The distinction between music and noise is mathematical form. Music is ordered sound. Noise is disordered sound.
Music and noise are both mixtures of sound waves of different frequencies. The component frequencies of music are discrete (separable) and rational (their ratios form simple fractions) with a discernible dominant frequency. The component frequencies of noise are continuous (every frequency will be present over some range) and random (described by a probability distribution) with no discernible dominant frequency.
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Sound is a longitudinal wave, which means the particles of the medium vibrate parallel to the direction of propagation of the wave. A sound wave coming out of a musical instrument, loudspeaker, or someone's mouth pushes the air forward and backward as the sound propagates outward. This has the effect of squeezing and pulling on the air, changing its pressure only slightly. These pressure variations can be detected by the ear drum (a light flexible membrane) in the middle ear, translated into neural impulses in the inner ear, and sent on to the brain for processing. They can also be detected by the diaphragm of a microphone (a light, flexible membrane), translated into an electrical signal by any one of several electromechanical means, and sent on to a computer for processing. The processing done in the brain is very sophisticated, but the processing done by a computer is relatively simple The pressure variations of a sound wave are changed into voltage variations in the microphone, which are sampled periodically and rapidly by a computer and then saved as numbers.
A graph of microphone voltage vs. time (called a waveform) is a convenient way to use a computer to see sound. Before the rise of ubiquitous digital computers, waveforms were often analyzed electronically using an oscilloscope — a cathode ray tube with an electron beam that traced voltage as a function of time on a fluorescent glass screen. Oscilloscopes are basically simplified televisions with one purpose (to a draw time series or parametric graph) and one color (usually bright green). This task is easily mimicked by 21st century desktop, laptop, and tablet computers as well as smart phones. Oscilloscope applications on these devices often pay homage to their analog ancestors by using a green color scheme.
The simplest sound to analyze mathematically is the pure tone — one where the pressure variation is described by a single frequency. A pure tone would look like a sine curve when graphed oscilloscope style.
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