independent of frequency. In practice however the resistive element varies with frequency. For instance, vibrations of most materials change their physical structure and so their physical properties; the result is a change in the 'resistance' equivalence. Additionally, the cycle of compression and rarefaction exhibits hysteresis of pressure waves in most materials which is a function of frequency, so for every compression there is a rarefaction, and the total amount of energy dissipated due to hysteresis changes with frequency. Furthermore, some materials behave in a non-Newtonian way, which causes their viscosity to change with the rate of shear strain experienced during compression and rarefaction; again, this varies with frequency. Gasses and liquids generally exhibit less hysteresis than solid materials (e.g., sound waves cause adiabatic compression and rarefaction) and behave in a, mostly, Newtonian way. Combined, the resistive and reactive properties of an acoustic medium form the acoustic impedance. The behaviour of sound waves encountering a different medium is dictated by the differing acoustic impedances. As with electrical impedances, there are matches and mismatches and energy will be transferred for certain frequencies (up to nearly 100%) whereas for others it could be mostly reflected (again, up to very large percentages). In amplifier and loudspeaker design electrical impedances, mechanical impedances, and acoustic impedances of the system have to be balanced such that the frequency and phase response least alter the reproduced sound across a very broad spectrum whilst still producing adequate sound levels for the listener. Modelling acoustical systems using the same (or similar) techniques long used in electrical circuits gave acoustical designers a new and powerful design tool. See also Soundproofing Acoustic attenuation Attenuation coefficient Anechoic chamber Acoustic wave Acoustic impedance References Acoustics