V.2 No 1

23

Homogeneous 1d resistant line

This result refines the conventional concept that at the overcritical regime the neighbouring elements vibration phase exceeds , ''so it is senseless to describe the phase displacements exceeding 180^o '' [14, p. 109]. Furthermore, at present there takes place a view that “in this connection, the values for which

have not a physical meaning” [14, p. 109] (where k is the wave coefficient, Boltzmann constant), and that “waves with the angular velocity more than _m  = 2v₀/a cannot exist in an imaginary 1-D crystal… Their wave vector, whose imaginary component causes a strong absorption, has to be complex. Thus, the frequencies for which the inequality > _m is true appear at the stop band” [14, p. 110]. The same in [15, p. 166]: ''Since a wave has its physical meaning only at the lattice points n, the wave having the argument ' = + /a describes just the same process as the wave with the argument  , so we will consider only the waves (in both directions) whose length is > 4a (here 2a is the lattice constant)". None the less, the above consideration shows that at the whole range (not only at the subcritical band) the delay phase does not exceed the limits of first Brillouin zone determined as

or _r = . The more, basing on the above solutions, we can show that not a standing wave, as it is conventionally thought, but a progressive wave exists in this line, as well as the along-line energy transfer exists. To make it sure, determine sequentially the dependencies of the phase velocity  v_f   and group velocity v_g on the frequency.