ABSTRACT
In narrow capillaries it is possible to have a situation in which the wavelength of the excitations becomes comparable to or greater than the diameter of the pipe. In that case, when helium flows, the normal part is stationary. It is then possible to have sound propagation in the superfluid part; these oscillations are called fourth sound. The velocity of fourth sound can be found from the linearized system of hydrodynamic equations in which one sets v n = 0. According to Eqs. 8-22 to 8-25 we have () ρ ˙ + ρ div v s = 0 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429502897/20d72e0b-9d39-4175-acc6-a943547edf8a/content/eq419.tif"/> () v ˙ s + ∇ μ = 0 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429502897/20d72e0b-9d39-4175-acc6-a943547edf8a/content/eq420.tif"/> () S ˙ = 0 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429502897/20d72e0b-9d39-4175-acc6-a943547edf8a/content/eq421.tif"/>
