Harmonic Overtones and Resonance

Decibel, or dB, is a logarithmic scale. A 3 dB change represents a doubling or halving of energy level, and a 10 dB change represents a tenfold change in energy level. The human ear perceives a 10 dB change as a doubling or halving of loudness. The intensity of sound diminishes with distance from the source of the sound at a rate of 6 dB, or 2², for each doubling of distance from the source of the sound.

The intensity of sound diminishes at a rate of 6 dB per octave on either side of the center frequency of a band-pass resonance. The intensity of sound diminishes at a rate of 12 dB per octave beyond the minus 3 dB cutoff frequency of high-pass and low-pass resonances. The initial falloff rate near the resonant frequency may be slower or faster than this, depending on how well damped the resonance is. Lightly damped high-pass and low-pass resonances will have a peak near the cutoff frequency and a faster initial falloff in amplitude. Lightly damped band-pass resonances will have a narrower bandwidth than heavily damped ones.

With equalizers and crossover networks a 12 dB per octave falloff rate with a high-pass or low-pass filter is called a second order response because the falloff rate is 6 dB × 2. With equalizers and crossover networks a band-pass resonance is also called a second order response, because it has two 6 dB cutoff rates, each on either side of the center frequency.