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Piano string excitation III: General solution for a soft narrow hammer

 

作者: Donald E. Hall,  

 

期刊: The Journal of the Acoustical Society of America  (AIP Available online 1987)
卷期: Volume 81, issue 2  

页码: 547-555

 

ISSN:0001-4966

 

年代: 1987

 

DOI:10.1121/1.394920

 

出版商: Acoustical Society of America

 

关键词: STRINGS;EXCITATION;MUSICAL INSTRUMENTS;ANALYTICAL SOLUTION;MECHANICAL VIBRATIONS

 

数据来源: AIP

 

摘要:

As an important preliminary exercise for understanding excitation of real piano strings, the general solution for a point hammer of massmhitting 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 complianceC0=m/16μTis 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 forCnot too close toC0.

 

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