By Karl F. Herzfeld
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Additional info for Absorption and Dispersion of Ultrasonic Waves
Gutowski, Ph. D. , Washington, / . Acoust. Soc. Am. 28, 478 (1956). , 1956; 10 A. Busala, D. Sette, and J. C. Hubbard, / . Chem. Phys. 23, 787 (1955). 11 T. A. Litovitz, T. Lyon, and L. Peselnick, / . Acoust. Soc. Am. 26, 566 (1954).  I. THE STOKES-NAVIER EQUATIONS OF HYDRODYNAMICS 47 experiments on helium and argon (see Sec. 47) seem to indicate that it is applicable though not completely so. 12 8. Formal Introduction of Volume Viscosity Except in monatomic gases and possibly monatomic liquids, the experimentally found absorption is always larger than the classical absorption «*iass> as s h o w n 1 b Y E q· (7~17)· As Tisza has first pointed out, this excess absorption can be formally accounted for by a volume viscosity; see Eqs.
At a viscosity of about 500 poise, this time is of the order of 10~~8 sec (in seven liquids). The "Lucas relaxation time/' which can be calculated from the low-frequency absorption and sound velocity, is between one-half and six times the relaxation time calculated from dispersion. The temperature coefficient of the high-frequency sound velocity is two to three times larger than that of the low-frequency velocity. 20 INTRODUCTION The absolute values of the high frequency (glass-like) shear and compressional modulus are then compared with those in a polymer, in quartz, in glass, and in a metal.
GENERAL THEORY OF RELAXATION IN FLUIDS  wants to exclude the bulk viscosity from P " , one must subtract from all the diagonal terms Ρ'~ the same scalar quantity chosen so that 1 PÏi + P22 + Pi's = 0. From Eq. (6-2) it follows that n n n I dU-, dUn dUo 1 \ = 2η (div w — div w) = 0. P'" is a scalar, the only scalar which can be built linearly from spatial differential quotients of the velocity components. The most general tensoi of the second rank is the sum of a proper tensor of the second rank and of a scalar.
Absorption and Dispersion of Ultrasonic Waves by Karl F. Herzfeld