Piano string excitation II: General solution for a hard narrow hammer
Donald Elliott Hall · The Journal of the Acoustical Society of America · 1987
As an important preliminary exercise for understanding excitation of real piano strings, the general solution for a point mass hammer hitting a perfectly flexible string is developed. The extensive literature on this problem is critically reviewed, and the previously known analytic theory presented in such a way as to emphasize its physical meaning. Use of a microcomputer to overcome the difficulties of multiple contacts between string and hammer is described, and representative results obtained by this method are presented. While this approach constitutes a general solution of the problem in principle, it is most practical for moderate values of the ratio of hammer mass to string mass. For extremely heavy hammers, it is argued that there is no good way to predict any details of the string energy spectrum without allowing for additional physical processes such as damping.