V.2 No 1

5

Transversal acoustic wave in gas

Actually, “the expression for the velocity u in a spherical wave has a form

where A is some constant, k is the wave number and  r is the distance from the radiator to the receiver

This expression presents a sum of two terms, whose role is different at different distances from the radiator: far from the radiator, at kr >> 1 (far field) the most important is the second term being proportional to 1/r. In this region the field of a pulsing sphere can be substituted by the field of a point source with the capacity, equal to a space velocity of the surface of a real source. The power of the point source is proportional to its capacity squared. Close by the source (kr << 1) the first term being proportional to 1/r² becomes essential. In this zone we cannot speak of the wave motion – the medium can be considered as ‘incompressible’ “ [6, p. 38]. “A sound field has different pattern at different distances from radiator. This holds true for any acoustic radiators, irrespective of their form: at the distance r >> d²/  (where d is the acoustic dipole length), the field of practically any acoustic radiator can be considered spherical, i.e. the sound pressure falls as 1/r. In this domain often named the Fraunhofer zone, the space-propagation of energy is defined by the direction characteristic. Close by the source, at r d²/ (Fresnel zone), due to the sound interference, the field has a complicated pattern” [ibidem, p. 39]. Proceeding from it, we can expect that the superposition of opposite-in-phase acoustic waves will also fall as 1/r  in the far from a source, which is typical to the acoustic wave in a free space.

The essence of the physical process on whose basis two longitudinal acoustic waves superposition can be considered as the transverse wave is the following. According to Fig. 1, in some local region, with two longitudinal dynamical pressures superposition, the resulting local dynamical pressure normal to the wave propagation direction forms. In its turn, it leads to the local displacement of the gas molecules in the resulting pressure direction, i.e. transversely to the wave propagation. This displacement itself, being completely similar to the shear, cannot induce the next molecules transverse displacement as it occurs, e.g., in solids, since in gas medium the necessary shear properties are absent. None the less, if the transverse acoustic wave propagation direction per se is formed by the sources of longitudinal acoustic field, then the resulting gas molecules oscillations will be transverse in all the wave propagation region. And these transverse displacements of the molecules will be local, in full accord with the local pattern of dynamical pressure exciting these oscillations. A membrane usually used as a receiver of longitudinal acoustic waves, if it had not the asymmetry, will not receive these oscillations, because the resulting longitudinal pressure is zero. The local transverse pressure will only turn the membrane, since the presence of this transverse pressure will mean the appearance of rarefaction – compression regions of gas medium, alternating alike the Karman vortex path [7]. So this wave can be registered only by the polarisation-type receiver, which could react to the presence of the rarefaction – compression in the direction, transversal to the wave propagation – i.e., by the polarisation acoustic dipole. Just this is why we can identify the studied wave with that transversal (polarisation).