SELF

16

S.B. Karavashkin and O.N. Karavashkina

3. Analysis of pattern of wave process in the near field of acoustic and EM fields

To make a good analysis, let us pay our attention that in both compared experiments we measure not some component of the delay phase of signal but the total delay phase of the wave process in space. This is important in view that in the conventional theoretic calculations of both acoustic and EM dynamic fields the general solution is usually presented as two summands, one of them decreases with the distance proportionally to   (1/r), and the second - proportionally to  (1/r²) . In the near field the first summand is mostly neglected, and the second is reduced to the form of standing wave. Earlier, in the introduction to [11], we showed this by an example of calculation of the EM radiator. The conclusions as to the near field of acoustic radiators are similar.

"When written out explicitly in terms of real and imaginary parts the two impedances are

(pulsating sphere)

These expressions are valid for all positions  r a , of course. At small distances (compared with the wavelength), kr << 1, both impedances are predominantly reactive, that for the pulsating sphere approaching    ₀a₀ikr and that for the oscillating sphere approaching   ₀a₀ikr/2 . Thus, in the neighbourhood of a small pulsating or oscillating sphere (or, by inference, near any small radiator) the acoustic field is largely reactive, the pressure being nearly out of phase with the particle velocity. The mean radial acoustic intensity, being , is proportional to the real part of the specific acoustic impedance" [16, p. 25]. However the experiments show that we should divide the field into the near and far regions not by the criterion  kr << 1  and kr >> 1, but by  r < (6 10)  and   r > (6 10) , since in the near region the delay phase of wave process has the complex dependence on the distance, and this reflects on the phase velocity. At first the phase velocity is large and abruptly diminishes to the end of this region. To the point, this is the region in which it is done to think the acoustic impedance pure imaginary, as corresponds to the absence of phase velocity. However the experiments show the opposite: the phase velocity is here not so large, and in the beginning of this region it can exceed the value of steady-state velocity in the far field. In the middle region of the near field, the phase velocity does not vanish, but considerably diminishes. This corresponds to the large delay phase (the phase velocity vanishing would mean the infinite delay phase that corresponds to the long-range effect), which in the third region falls a little, and in the end of this region the phase velocity stabilises at the level corresponding to the value known for the far field.

Thus, on one hand we see a full consistence of experimental results for the near field of acoustic and EM fields, and on the other hand, we see the conventional theoretical approaches to the fields calculation inconsistent with the experimental characteristics. For acoustic fields of single pulsing spheres, as shown in [20], the near field is described by the dynamical non-conformal mapping of a unit half-stripe in the plane  Z  into plane  W . The superposition of such spheres some distanced and oscillating in anti-phase can serve as the model for a radiator of transverse acoustic wave. This means, the field of transverse wave in complex record has to be described by functions non-analytical after Caushy - Riemann, but analytical in general meaning, according to definitions given in [21].

For the near field of EM dynamical field, the semi-empirical regularities already exist. With the analogies between the acoustic and EM dynamic fields they can be essentially enhanced.

The principal advantage of the described analogy is that it lifts the discrepancy between the gas-like properties of aether and properties of EM fields.

3. Conclusions

We have correlated the pattern of wave process in the near field of acoustic transverse wave and EM wave. We showed that in both cases the near field divides into three typical regions. In the first region bordering with the radiator, the phase velocity is higher than that steady-state in the far field; it falls fast in transition to the second region. In this second, the phase velocity is minimal (but not zero), and the value of minimum depends, most probably, on the impedance of reflecting surface. In the third region, the phase velocity grows, and at  r = (6 10)   it stabilises at the value typical for the far field. In this way we completely lifted the discrepancy between the gas-like properties of aether and properties of EM wave.