V.4 No 1

37

Study of dynamic scalar potential

6. Investigation of acoustic fields with the method of deforming grid

For the final example, let us broaden the application of the method of deforming grid to the acoustic fields.

There in this area also exist many unclear points and incorrect interpretations of physical phenomena caused by this reason. In particular, as shown in [17], an incorrect idea that in media free of shear deformation transverse waves cannot propagate, limited the area of studies in acoustic processes in gas media and disabled the researchers to develop their knowledge of many properties of fields in gas media. And even after we published [17], the lack of visualisation of transverse waves in media free of shear deformation prevented most of scientists to grasp the essence of processes in transverse acoustic waves.

To visualise the propagation of transverse acoustic waves, consider the acoustic dipole consisting of distanced in space two classical spherical radiators oscillating in anti-phase. The schematic diagram of calculation of such dipole will little differ from the above study of EM dipole in the item 3.

To find the expression describing the radiation of each of half-oscillators of dipole, we will use the results yielded in [18]. As showed in that paper, displacement of elements of gas continuum occurs along the radius from radiator; it is described as follows:

where r is the momentary shift of elementary volumes of gas continuum distanced at r₀  from the centre of spherical radiator.

The expression (56) allows to plot the diagram of dipole radiation. For it, we have to suppose that all elementary masses of gas continuum are concentrated in the nodes of our transforming grid, and these nodes shift in time accordingly to the geometric sum of shifts which each half-oscillator produces at the given point of space.

The diagram of resulting oscillations for a half-wave oscillator is shown in Fig. 25.

Fig. 25. Diagram of propagation of acoustic waves excited by a half-wave oscillator

In this diagram we first of all see, in direction of normal to the line of oscillators there propagates just such wave as we saw in case of electric dipole. As the result of superposition of waves from the half-oscillators, there has formed an usual transverse wave with all properties attributed to this type of waves. And naturally, in the superposition of two potential fields in gas medium, shear properties have not revealed. None the less, gas medium behaves the same as the medium having the property of shear deformation. This fully corroborates the conclusions of [17] that to excite transverse waves, the shear ability of medium is not necessary.

Finally, this diagram shows that half-oscillators actively affect each other, whereupon their surface falls off from the spherical shape, this considerably affects the formation of an integral transverse wave in the far field and changes the wave impedance to the radiation of each half-oscillator.