SELF

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S.B. Karavashkin and O.N. Karavashkina

However along with this statement we come back to the stumbling-block between the transverse acoustic and EM waves, since as long ago as Aragoe and Fresnel had established the EM wave strongly transverse. This fact has been reflected and consolidated in the Maxwell equations formulated on the basis of hydrodynamic theories - theories describing the dynamic processes in media unable to transmit the transverse oscillations.

Actually, in the modern treatment, the EM wave transverseness is conventionally proved so: "Consider a plane wave running in positive direction of the axis  x ; in such wave all values, and particularly  , are the functions only of  [t - (x/c)] . From the formulas

where the stroke means the differentiation with respect to [t - (x/c)] , and    is the unit vector along the wave propagation. Substituting the first equality into the second, we find that

We see that the electric and magnetic fields    and    of the plane wave are directed perpendicularly to the wave propagation" [10, p. 147].

However, as is shown in the paper by one of the authors [11], the lack of rigour in that proof of transverseness results from the fact that the inaccurate relation between the vector and scalar potentials was used in the conventional formalism, and the calibration excluding the scalar potential from the equations of dynamic fields was used as well. If we take into account these facts, the rigour of the proof breaks.

But the main problem of Maxwell equations is, by force of objective reasons of the hydrodynamics level accessible in 19th century, when Maxwell was deriving his famous system of equations, he could ground on the conservation laws only for stationary fields proved by that time. As we showed in [12] and [13], in dynamic fields the conservation laws essentially change, and this completely lifts the bans on longitudinal EM waves existence. The fact of their existence has been established not only theoretically in the above papers but experimentally [14] on the especially developed device radiating the directed longitudinal EM wave in free space in the 30 kHz band. In this way we lifted a number of contradictions that prevented from introducing the proper analogy between the EM and acoustic waves. But the problem connected with the transverse acoustic waves remained.

To surmount this problem, we have proved theoretically [13] and corroborated experimentally [15] that the transverse acoustic waves propagation has been banned because of supposition that the transverse component can arise exceptionally due to the transverse oscillations of the source. Up to now no one researcher supposed possible to form a transverse acoustic wave resulting from the superposition of anti-phase oscillations of the sources of longitudinal wave, as it is done in electromagnetism.

Fig. 2. General diagram generating transerse acoustic wave in gas medium

Given the said factor and the scheme realised on the basis of superposition interaction (see Fig. 2), the necessity of shear deformation of medium fully falls away. As shows the theory and corroborates the practice, there in the medium not only arise momentary transverse local dynamic pressures but appear the corresponding transverse shifts of the elements of medium. As we showed in [13], the value of this local transverse velocity of the gas medium for the scheme presented in Fig. 2 is

where = ₁ =  ₂ ,  (r, t)  is the longitudinal dynamic potential created by each source, and  v   is the amplitude of the longitudinal velocity of oscillation of medium under affection of each source separately.