Wave Motion 31 (2000) 93–96 Discussion Comment to “A new formula for the velocity of Rayleigh waves” by D. Nkemzi [Wave Motion 26 (1997) 199–205] Peter G. Malischewsky ∗ Friedrich Schiller University, Institute of Geosciences, Burgweg 11, D-07749 Jena, Germany Received 27 May 1999 Abstract A new formula for the phase velocity of Rayleigh waves for all Poisson values by Nkemzi [Wave Motion 26 (1997) 199–205] is discussed and commented. By applying Cardan’s formula and using the advantages of mathematica the author succeeds in extracting a formula which is also valid in the whole range of Poisson ratios and is, contrary to Nkemzi, as well correct as probably the simplest representation of the relevant real root of Rayleigh’s equation. Additionally, a similar formula is presented for the complex roots. In this connection, for the first time an analytic expression of the critical Poisson ratio, which limits the range of complex roots, is derived. ©2000 Elsevier Science B.V. All rights reserved. It is interesting to realize that Rayleigh’s famous formula, which was already found more than 100 years ago, attracts attention from time to time. This fact also emphasizes the brilliancy of Lord Rayleigh [4], who had predicted theoretically the existence of surface waves in an homogeneous half-space subsequently named Rayleigh waves. While the simple numerical availability of all kinds of roots of Rayleigh’s equation is undisputed it may hold some fascination to look at the problem from a deeper point of view to get insight into the behaviour of elastic material at all. It should not be forgotten that the existence of such critical dimensionless parameters as presented later on may have a deeper reason which we do not understand until now. The paper by Nkemzi [2], which is under discussion here, presents a new form of the solution of Rayleigh’s equation by demonstrating the power of the theory of complex functions. Unfortunately, the final result as printed in Nkemzi’s paper is incorrect. This can be easily demonstrated by using a mathematica program. The fact is not astonishing because the extraordinary complexity of Nkemzi’s formula virtually asks for misprints and misunderstandings. However, it is to be demonstrated here that such a complexity is actually not necessary to express the solution of Rayleighs equation in a closed and simple form as a continuous function of the parameter γ , γ = β 2 α 2 = 1 − 2ν 2(1 − ν) , (1) ∗ Present address: Universidad Nacional Autonoma de Mexico, Instituto de Investigaciones en Mathematicas Aplicadas y en Sistemas, Apdo. Postal 20-726, 0100 Mexico DF, Mexico. E-mail addresses: mali@leibniz.iimas.unam.mx; mali@geo.uni-jena.de (P.G. Malischewsky) 0165-2125/00/$ – see front matter ©2000 Elsevier Science B.V. All rights reserved. PII:S0165-2125(99)00025-6