In this case the noise's band is theoretically infinite, but for our purposes it will suffice to consider the frequency segment that we're most interested in, namely, our usual theoretical audible frequency spectrum: 20 Hz – 20 KHz.
This kind of noise is generated by the heat that is intrinsic to any electronic piece of equipment. The heat provokes collisions between the electrons in all directions and at all speeds, thus generating currents at all kinds of frequencies. These frequencies' amplitudes, in other words the currents' intensities, are relatively constant seeing that the collisions' directions are absolutely random. Thermal noise increases as temperature does, because the kinetic energy tied to the particles also increases proportionally to it.
What we mean by white noise is a noise with a constant amplitude covering the whole frequency spectrum. Essentially it is thermal noise, but with the difference that in this case the noise has been specifically generated for testing purposes. Indeed to test the behaviour of a piece of audio equipment, a mixer's channel for example, you'd send white noise through the input and observe the signal at the output. Generally the aim is to have an output-signal that is relatively constant at all frequencies, which tells us that the equipment is trustworthy, again, at all frequencies. Normally white noise is used to test electronic equipment.
The following is a sample sound of white noise:
Seeing that white noise is constant at all frequencies, this means that the energy in each octave is not constant. For example, the energy present in the 20 Hz- 40 Hz band won't be the same as that present in the 5 KHz - 10 KHz band. Clearly the latter band will have far greater energy, even if its width is still one octave whereas the second frequency interval is far wider than the first one; in other words it contains more frequencies and therefore more overall energy.
Pink noise, which too is used for testing purposes, is characterized by a 3dB drop every time frequency doubles. This way the energy of each octave stays constant over the whole spectrum. It is often used for calibrating sound reinforcement systems when white noise doesn't sufficiently correspond to the characteristics of the signal which will feed the P.A. This is due to the fact that an audio signal has a lower energy content at high frequencies than at low frequencies, and is therefore badly simulated by white noise whose energy in each octave doubles the previous one. The following diagram compares the frequency spectra of a white noise and a pink noise:
The following is a sample sound of pink noise:
As we can clearly hear, this noise has a smaller high frequency content than white noise does.
For thoroughness' sake let's take a brief glance at red noise too. It has a rate that is somewhat similar to pink noise, apart from the fact that it has a 6 dB drop (rather than 3 dB) every time frequency doubles. Sometimes red noise is chosen for testing a sound reinforcement system with an even smaller stimulation of high frequencies.
The following is a sound sample of red noise:
As we can clearly hear, this noise's high frequency content is smaller than pink noise, and, it goes without saying, smaller still than white noise.