What is the difference between music and noise? We can define music as organized sound. It can be organized melodically, rhythmically, and harmonically.
There is another, more basic difference between music and noise. This is a difference we can both hear and see. The sound waves that noise creates are very unorganized. Look at the graph for the noise sound wave, it keeps changing. But the sound waves for musical sounds are organized. The sound waves repeat. That's what makes a sound wave have a pitch. The sound wave below is very simple and really doesn't sound very pleasant - kind of sounds like a bad computer voice. But it does have pitch.
To learn more about sound waves and the science of sound, check out the following web links.
Acoustics for Music Theory
Frequency, Wavelength, and Pitch
Timbre: The Color of Music
Harmonic Series