V.3 No 1

15

Comparison of characteristics of propagation velocities

"The above formulas and plots allow to calculate the differential phase velocity which by definition is equal to

(here  = [(/c)r + *(r)] [(/c)r + (r)]  is the wave phase) or, noting that for the air n =1, we have

Considering the curves _z  in Fig. 3, we see that in the near of "lengthened" antenna  d_z /dr 0 , so that here  v ; for the "shortened" antennas d_z /dr  goes through the minimum so that  v  has here the maximal value. Further, with the increasing distance,  v  falls, and at r    in order to calculate  v  we have to use already the formula (20). Then the value  v  becomes less than  c/n  and reaches the minimal value which is the smaller (at  f = const) the less the conductance    is. After it,  v  increases monotonously, tending to the constant limit  c/n  [19]. This result is practically important. It demonstrates that the radio waves dispersion over the earth surface is negligibly small, and irrespectively of its electric properties, the phase velocity at quite large distances from the radiator tends to the radio waves velocity in the air" [18]. The results of measurement of the differential phase velocity of radio waves at  = 120, 180 m   are shown in Fig. 4.

Fig. 4. Experimental result of measurement of the phase velocity of radio waves = 120, 180 m [17, p. 845, Fig. 123.2]

To compare the pattern of velocity variation in EM and acoustic fields, in Fig. 5 we present the experimental regularity of the phase velocity against the distance for the acoustic transverse wave from [15, Fig. 8].

Fig. 5. Experimental plot of phase velocity of transverse acoustic wave propagation in the air against the relation r/ at f   = 7,4 kHz [15, Fig. 8]

We see in these plots that in both fields immediately near the radiator the phase velocity is large and fast falls with the distance. Having transited the minimum, the velocity grows, and in limits (8 10)    the near field is over. In the far field the propagation velocity tends to the steady-state value. The difference in the depth of minimum is most likely caused by the fact that in the acoustic experiment the acoustic conductance of the base has been intentionally diminished as possible, to prevent the parasitic reflection of signal from the surface. This caused both a small value of minimum and some growth of the near field, in comparison with the EM field being the analogue.