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Piano hammer-string contact duration: How the bass hammer is released from the string

Stulov, Anatoli 

We associate the bass hammer-string contact duration with the time of propagation of compression wave traveling through the hammer body from the contact point to the hammer kernel and back. Based on the hereditary model of the microstructured wool felt, it has been revealed that the stiffness of felt is a nonlinear function of the compression, and it is strongly determined by the rate of the felt loading. This means that the speed of the compression wave that propagates through the felt depends on the wave form and on its amplitude. It has been shown that the pulse of a smooth form, and which has no discontinuity on its front propagates with the constant speed until the accumulation of nonlinear effects results in the eventual continuous wave breaking. After that moment the shock has been formed, and now the velocity of the shock wave depends on the value of the jump discontinuity across the wave front. It has been shown that the front velocity of the shock wave is greater than the velocity in a linear medium. Therefore, the total time of wave propagation, which is related with a duration of the hammer-string contact, decreases as the dynamic level of the hammer impact is raised. As result, for the first bass hammers, the contact duration is shorter than the round-trip time to agraffe, and hence, no reflected wave is needed to assist the hammer for going away from the string.