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Karl F. Herzfeld's Absorption and Dispersion of Ultrasonic Waves PDF

By Karl F. Herzfeld

ISBN-10: 1483230570

ISBN-13: 9781483230573

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61, 531 (1942). 2 L. Mandelstam and M. Leontovic, Compt. rend. acad. set. S. 8, 111 (1936); Zkur. Eksperth. i Teoret. Fiz. 7, 438 (1938). 3 For example, in glycerine at — 20° C and 30 Mc, a is about 4 cm"*1, λ = 1/200 cm, and α(5Β/ω) ~ 1/300 cm. 48 A. GENERAL THEORY OF RELAXATION IN FLUIDS [8] The processes responsible for the excess absorption are "relaxation" processes. A general discussion of such processes is given in the next section. In pure substances two types of relaxation phenomena are known to produce excess sound absorption.

A similar statement applies to the recompression of rarefaction regions. , sound absorption. Equation (4—3), taken for unit volume, has to be supplemented, on the right side, by the heat conducted in a second, which is (λ = heat conductivity) d2T It should be remembered that Eq. (4—3) applies to 1 mole. Therefore, Eq. (4—4) is now to be written (with cp referring to unit mass) dT τβ ^n dp ^-ΪΓ- -ί „ d 2T λ tm nx (7 3) = Ί^' ~ In the absence of dissipative effects (Sec. 5) it is possible to satisfy the equations with an undamped wave.

Now Writing total differentials m, f dH nh-Ct and (f)r=-(a+-· (4-4) [4] I. THE STOKES-NAVIER EQUATIONS OF HYDRODYNAMICS 31 Therefore, Eq. (4—3) can be rewritten as the general equation of the isentropic variation (5 constant) '(£),*-* C,dT-T{w)ip = 0. (4-6) Equation (4—3) only presupposed adiabatic conditions (dQ = 0). Equation (4—5), however, presupposes reversibility. Equation (4—6) can be rewritten as \dp)s TV-ß-. (4-7) This is the equation connecting temperature and pressure change in an adiabatic reversible compression for any fluid.

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Absorption and Dispersion of Ultrasonic Waves by Karl F. Herzfeld

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