Impulse and response

[Sarah Fox]

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Hi David,

Your point is well taken, but there are still other factors than the key =
leading.  There's also gravitational acceleration on the hammer, =
partially counterbalanced by gravitational acceleration on the key =
leading and other key parts, and partially counteracted by upward force =
from the back rail (transferred with various mechanical advantages =
through the keystick, capstan, wippen, etc.).  A certain amount of force =
on the keystick (DW) will be required to counter the gravitational =
acceleration.  It is the force beyond the DW which accelerates the =
hammer from rest.  With a heavy hammer, there's indeed more leading to =
achieve a target BW, but there's also more gravitational force to =
counteract, so it's a draw. =20

Given two keys with different weights of hammers but balanced with the =
same DW, the same force will accelerate the hammers at different rates, =
but the kinetic energy in the hammers will be the same, resulting in the =
same impact force and the same amplitude of note.  With the slower =
moving (heavier) hammer, the impulse will have spectral content of lower =
frequencies, resulting in a darker sound.

Peace,
Sarah

PS I've ignored the lesser factor of key inertia (from more extensive =
leading for heavier hammers), but that's a big ol' can-o-worms over =
which nobody seems to agree.  ;-)

----- Original Message -----=20
  From: David Love=20
  To: 'Pianotech'=20
  Sent: Sunday, October 03, 2004 7:07 PM
  Subject: RE: Impulse and response


  Thanks for the post Sarah:

  =20

  The only problem with this part of the analysis is that we are really =
talking equal acceleration not equal force applied to the key.  Since a =
heavier hammer would, presumably, have more lead in the key (if the =
balance weight was the same) then an equal amount of force applied to =
the key by the finger would net out to the same acceleration of the =
hammer (flexing and friction aside).  The point being that it's the =
acceleration that counts.  If the two hammers are accelerated equally, =
which is what happens in practice, then by f=3Dma, the force imparted to =
the string would be greater with the hammer with more mass.=20

  =20

  David Love
  davidlovepianos@comcast.net=20

  -----Original Message-----
  From: pianotech-bounces@ptg.org [mailto:pianotech-bounces@ptg.org] On =
Behalf Of Sarah Fox
  Sent: Saturday, October 02, 2004 9:23 AM
  To: Pianotech
  Subject: Impulse and response

  snip.

  =20

  Mass of the hammer:  As Bernhard alluded, a heavier hammer will move =
more slowly than a lighter hammer, given the same energy delivered at =
the key.  The collision will therefore be slower, the felt compression =
will be slower, and so the ramping of force will be slower.  A heavier =
hammer should result, therefore, in a darker sound.

  =20

  .

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