Absorption and Dispersion of Ultrasonic Waves by Karl F. Herzfeld

By Karl F. Herzfeld

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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.

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. (6—1) and (6—3). The equation of motion, Eq. (7 — 1), is then replaced by [see Eq. (6—8)] du dp U dp , d \ \d2u du 2 du dp 4/. , 3 du\ \d2u la „ The rest of the calculation proceeds as before, and an expression like that in Eq.

GENERAL THEORY OF RELAXATION IN FLUIDS [9] On applying to the particle a periodic force F0etttit, instead of the steady force, the motion will be periodic with the frequency ω of the impressed force once the transients have died out. The solution is F0 eiu>t x = m(œ02 — ω 2 + ίωω') (9-4) with the abbreviation ω' = bjm. FIG. 9-1. In-phase displacement as function of the frequency of a simple harmonic force. Curve A, resonance; curve B, relaxation. If one has an electromagnetic wave propagating through a medium made up of N such oscillators per unit volume, each with charge e, one gets a complex refractive index n* (W*)2 _ 1 = 4πΝ m ω 0 2 — ω 2 + ιωω' (9-5) which can be split, if the absorption is not too strong, into the real refractive index and the absorption " — ( * ) ■ - ' - 4πΝβ2 m ωΛΛ — ω" (ω 0 2 - ω 2 ) 2 + ω 2 (ω') 2 (9-6) [9] II.

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