I have seen a previous answer related to my question but am not clear if the practical situation I am describing pertains.
Let's say we have to strings fixed at both ends. Both strings are the same material. One string is 1 meter in length, the other is 1.5 meters in length.
Now lets say we apply a violin bow to each with identical physical motion and energy being applied. I think it is possible to predict a difference in the frequency of the resulting sound, and that the shorter string will sound at a higher frequency.
Is it also possible to predict that the shorter string will have either a higher or lower amplitude than the longer string? Or will they be identical, or dependent upon externalities pertaining to human perception (e.g., Fletcher/Munson curves, or the characteristics of dampening when sound travels through air)?
In relation to the linked answer, can the identical bowing mechanism be considered a constraint?
Intuitively, it seems to me that it would be more "work" to move a surface twice as much in a given time interval.
But perhaps in this case, the amount of work also relates to the length of the string (i.e., more work to move a longer piece of string) and the amplitude relationship would have to also take that into consideration?
Another situation I am thinking about is that of a woodwind, with an identical amount of force applied to the mouthpiece via breath pressure but the fingerings (length of air column) changed. Can we predict in this case if the higher note will be either quieter, louder or the same volume as the lower?
In the case of the oboe (which I play) identical work results in the higher notes being considerably softer, and technique demands that the oboist work harder (use more air pressure) on notes that have higher frequencies than on lower notes to get equivalent volumes. I am trying to better understand why this is a requirement of oboe technique.
(I thought the string example might be more familiar and easy to explicate, as most people are unfamiliar with the oboe reed. But the two examples may be quite orthogonal.)