Brownian motion apart once the particle is in motion. Also, there would be a distribution of different possible Δ"V"s instead of always just one in a realistic situation. The diffusion equation yields an approximation of the time evolution of the probability density function associated to the position of the particle going under a Brownian movement under the physical definition. The approximation is valid on short timescales. The time evolution of the position of the Brownian particle itself is best described using Langevin equation, an equation which involves a random force field representing the effect of the thermal fluctuations of the solvent on
Brownian noise it has more energy at lower frequencies, even more so than pink noise. It decreases in power by 6 dB per octave (20 dB per decade) and, when heard, has a "damped" or "soft" quality compared to white and pink noise. The sound is a low roar resembling a waterfall or heavy rainfall. See also violet noise, which is a 6 dB "increase" per octave. Strictly, Brownian motion has a Gaussian probability distribution, but "red noise" could apply to any signal with the 1/"f" frequency spectrum. A Brownian motion, also called a Wiener process, is obtained as the integral of