Ratio of force to amplitude & decay of harmonics a constant?

[Jake Jackson]

Sorry if the answer to this is too self-evidentally "yes":

In "acoustic" instruments, is the ratio of force to the amplitude and duration of all partials linear? (Neglecting, intentionally, the effect of wood, etc: I'm speaking only of the initial sound source, not other contributing reflections, absorbtions, etc.)

In other words, if I hit a guitar string with an increasing velocity of +1, will the fundametal and each partial always increase in amplitude and duration by the same factor until I reach the quadratic effect? Or is the answer dependent on the exact make-up of the oscillator,which may itself be better able to create some frequencies better than others, so no rule applies?

But if the situation were ideal,and the perfect string was able to produce all frequencies, would the increase in amplitude and duration of the partials be linear?

(And can someone point me to a good source of information about the quadratic effect?)I'm not developing an instrument. I'm only trying to better understand the acoustics of instruments.

[jupiter8]

The higher partials drop off faster than the lower.

[Jake Jackson]

With an increase in force? (Or are you just speaking of the rate of decay after any given velocity?)

[BertKoor]

You could load a sustained piano sample (a single note or an end chord of a recording, or from a piano sample library that's made without looping) and perform spectral analysis on it, e.g. with Adobe Audition / CoolEditPro. You should see that higher harmonics have less sustain and die out faster.

[Jake Jackson]

(Why are people telling me that higher harmonics decay faster than low harmonics? I know that. It is unrelated to my question.)

[Teksonik]

[Jake Jackson]

I was asking the question out of a desire to learn the answer.