Piano string excitation III: General solution for a soft 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 hammer of mass m hitting a perfectly flexible string of linear density μ is developed further by allowing for hammer compliance. Previous work on this problem is critically reviewed, and the existing analytic theory is summarized. The role of the critical compliance C0=m/16μT is discussed, and inclusion of a resistive force is also considered briefly. In close parallel with our earlier general solution for a hard hammer, the analytic solutions are implemented with a microcomputer to overcome the difficulties of multiple contacts between string and hammer, 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 and for C not too close to C0.