By Karl F. Herzfeld

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This similarity is due to the fact that for the sound wave at high frequencies the shear forces predominate over the compressional forces while propagation of the electromagnetic waves is governed by ohmic resistance, formally analogous to a viscous force. In liquids, no experimental case has yet been found in which the viscosity does not drop off because of relaxation before the condition shown in Eq. (7 — 13) is reached. If heat conductivity is not neglected, instead of the adiabatic equation Eq.

2—3) have the great disadvantage of being nonlinear. For instance, Eq. (2—1) contains the product of p and w\ Eq. (2—3), due to the form of D/Dt, even contains triple products like pu^dUjjdx^) This nonlinearity, which makes the principle of superposition inapplicable, is mainly responsible for the complexity of aerodynamics. [3] I. , s, w, are small and This means that in Dp of the fluid in the absence of the sound wave. that all quantities characteristic of the sound wave, all products or powers above the first are neglected.

7—5") and (7—5'"), the classical expression, Eq. (4—10) 1 yKT P-Po 1 A> V where 930 is the velocity at low frequency. Equation (7—7) can then be written 1 W ω ) [ 3 /o0S802 \ 93 ω ) (7-7') In first approximation, if (α93)/ω 0 V _ or 93 = 93ft * = 3^ n' 1 ω'. PoV (7-8) For very high frequencies, a more exact evaluation has to be made. Define with Lucas3a a time 3b TL = 4 η 3~/>oV 4 >7 ~ ^ /c r .

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Absorption and Dispersion of Ultrasonic Waves by Karl F. Herzfeld


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