English translation

The critical behaviour of the correlation length ξ is given by:

These relations embody the central idea of dynamic scaling theory. The objective, however, is to describe ultrasound absorption in three-dimensional critical binary fluids. A corresponding expression for sound attenuation must therefore be obtained. Renormalization-group theory and an ε-expansion yield:

with

Bhattacharjee and Ferrell subsequently established the final relation between the absorption per wavelength (αλ), the temperature-dependent amplitude A(T), and a scaling function F(Ω):

The remarkable feature of F(Ω) is that it depends only on the reduced frequency Ω = ω/ω_BF. This frequency can also be written as:

where Γ = ω_BF. The amplitude is given by:

In physical terms, if the temperature dependence of A or  is weak, F(Ω) expresses the ratio of excess attenuation near the critical point to attenuation at the critical point itself:

Original mathematical notation preserved from the thesis.