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Dynamic phenomena

The expression for the sound velocity of a liquid,

contains the bulk modulus K. If K is frequency-independent, then the liquid behaves as a linear medium, so that sound propagates without dissipation or mode coupling. In reality, all liquids show some dispersion: with increasing frequency, K crosses over from the low-frequency, liquid-like limit K 0 {\displaystyle K_{0}} to the high-frequency, solid-like limit K ∞ {\displaystyle K_{\infty }}. In normal liquids, most of this crossover takes place at frequencies between GHz and THz, sometimes called hypersound.

At sub-GHz frequencies, a normal liquid cannot sustain shear waves: the zero-frequency limit of the shear modulus is 0. This is sometimes seen as the defining property of a liquid. However, like the bulk modulus K, the shear modulus G is also frequency-dependent and exhibits a similar crossover at hypersound frequencies.

According to linear response theory, the Fourier transform of K or G describes how the system returns to equilibrium after an external perturbation; for this reason, the dispersion step in the GHz to THz region is also called relaxation. As a liquid is supercooled toward the glass transition, the structural relaxation time exponentially increases, which explains the viscoelastic behavior of glass-forming liquids.