By Karl F. Herzfeld
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Extra resources for Absorption and Dispersion of Ultrasonic Waves
53, 899 (1938). I. 551'5b The effect of viscosity on sound absorption was first calculated by Stokes, that of heat conductivity by Kirchhoff and Langevin. The exact solution of the combination of Eqs. A! = ^ J - . (7-20) 4 ODTL ηω One other dimensionless quantity is of importance here. number [Pr] [Pr]=g The Prandtl (7-20') 5a I t follows from Eqs. (7 — 16, 7—18) as Herzfeld and Rice have pointed out, 5 b t h a t — contrary to opinions expressed in the past — a sound wave behaves more and more adiabatically and isentropically, the lower its frequency is.
It is then possible to calculate from sound absorption a relaxation time which is much longer than Hall's, but still not measurable at present. INTRODUCTION 17 The absolute value and the temperature dependence of ultrasonic absorption in water tell us that under the assumptions of the two-state theory, the two states are present in the ratio of about 1:3, and that this ratio is nearly temperature independent, but they do not tell us whether the state present in the lower amount is the one with the larger or smaller specific volume.
However, this effect is, in general, small. If η were zero, one would have (s)' 4 = l + (y-l)(5-y) CpJ (2p0*2)2 (7-19) Equations (7—1) and (7 — 3) have a second solution which represents a strongly damped "temperature" wave. See K. F. Herzfeld, Phys. Rev. 53, 899 (1938). I. 551'5b The effect of viscosity on sound absorption was first calculated by Stokes, that of heat conductivity by Kirchhoff and Langevin. The exact solution of the combination of Eqs. A! = ^ J - . (7-20) 4 ODTL ηω One other dimensionless quantity is of importance here.