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Download PDF by Karl F. Herzfeld: Absorption and Dispersion of Ultrasonic Waves

By Karl F. Herzfeld

ISBN-10: 1483230570

ISBN-13: 9781483230573

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The subject is still in its infancy. For relatively few liquids are all the data available and, in the historical development, at the beginning not all necessary measurements were made. As a consequence, it is necessary to describe in detail the individual, relatively scarce, measurements and then try to draw conclusions by generalization. Sections 106 and 107 give the experimental results for the propagation of longitudinal waves in glycerine and w-propyl alcohol as a function of temperature and frequency, and the interpretation of these data along the lines just discussed.

2—1) and 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.

The energy equation is then used, expressing the fact that any work done on the element goes toward increasing the internal energy or dE=-pdV=- d(pV) + Vdp d(E + pV) = Vdp. E + pV is the enthalpy or heat content, H. 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).

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Absorption and Dispersion of Ultrasonic Waves by Karl F. Herzfeld

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