hammer momentum physics

[Helmut Wabnig]

The kinetic energy of a moving object is: (mass.velocity.velocity)/2

A hammer of half mass must strike with greater velocity.

velhalfmass = velmass.sqrt(2)

Don't confuse "energy" with "impulse". We are converting kinetic
energy from the moving hammer into sound energy.
(This is veryvery simplified, as the hammer is bouncing back,
and also some thermal losses occur.)

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