Comments on the paper: Waves produced by a pulsating source travelling beneath a free surface
There appears to be an error in the analysis performed in the subject paper by Dr. Tan [1], which has led to erroneous conclusions in regard to the character of the resulting wave pattern and the asymptotic conditions at infinity that are used to arrive at a unique solution. Other treatments of this same problem have been carried out by Becker [2], Kaplan [3], and Wu [4], and they have arrived at different conclusions from those of Tan. Their results show two harmonic wave trains on the downstream side of the source when r > j, corresponding to the roots K:t and Ki , in agreement with the results of Tan. However, when 0 < r < }, Tan indicated that four harmonic wave trains were on the downstream side, with no disturbance found to propagate to infinity upstream. This led to his conclusion that the imposition of an asymptotic upstream condition of "vanishing disturbance at infinity" is sufficient to render his solution unique. The results of Becker, Kaplan and Wu were all in agreement, and showed that when 0 < r < J there were three harmonic wave trains on the downstream side, and one harmonic wave train on the upstream side. It can be shown that the wave in the upstream side corresponds to the root K2 and that the error in Tan's analysis was not recognizing the fact that, in the notation of [1],