Abstract
Weinstock [Amer. J. Phys. 38, 1289 (1970)] has studied the problem of the propagation of a particular disturbance on a one-dimensional semi-infinite lattice of similar atoms, coupled by nearest-neighbor ideal springs; a solution to the same problem, in infinite lattice form, was given earlier in a book by Morse and Ingard [Theoretical Acoustics (McGraw-Hill, New York, 1968) p. 91]. The problem is essentially the following: Given a one-dimensional lattice that is stationary for all times t<0, what is the response of the lattice if one of the atoms (the end atom in the semi-infinite lattice case) is constrained to move with constant velocity for all t≥0? The method of response functions was developed by the author [J. Phys. Chem. Solids 23, 1269 (1962)] to solve related problems involving n-dimensional infinite and semi-infinite lattices; a summary of this method is presented for the special case of the one-dimensional lattices, and it is shown how it may be used to solve this problem in a slightly more general form.
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