hammer momentum physics

[Michael Wathen 556-9565]

>>>>>>>>>>>>>>>

Excitation of an oscillation with a step-function:
The string will be displaced locally by the hammer.




heavy hammer:

        ..........................     step amplitude
        .                        .
        .                        .
        .                        .
        .                        .
        .                        .                       time axis
........                        .............................



light hammer:


        ...........
        .         .
        .         .
        .         .
        .         .
        .         .
        .         .
        .         .
        .         .
        .         .
        .         .
        .         .                                      time axis
........         ............................................



The area beneath the curve is a measure for the energy and has to
be the same for heavy or light hammers to deliver the
same excitation energy.
Shorter aperiodic pulses will have more harmonics and less
fundamentals due to Fourier Analysis.
The sound of the string will be different. More high harmonics
and less fundamentals will be excitated.
But we have to consider this:
"Loudness" is a function of our ear. It does not linearly
correspond to the amplitude distribution of the sound spectrum.

This is as simple as I can make it. Don't beat me for boring you.
It was a nice typing exercise.
See you later,
>yours
>Helmut Wabnig
>wabi@net4you.co.at


Helmut,

I spent all of last Winter taking Fourier Analysis.  So I
would like an explanation of why the lighter hammers produce more
higher harmonics and less funadamental.  It would seem to me that
after short period of attack the energy would distribute itself
equally amoungst all the normal modes in a way that is characteristic
of the string and independent of the initial shape of the impulse.
I have heard what you are claiming before but I have never quite
grasped it.

Michael Wathen