There are several reasons why we should use this technique instead of just playing real musical instruments.
For example, for people who build instruments, they could simulate various changes in an instrument (shape, material etc …), to already know how it would sound, without actually building it. This would reduce costs and production times.
Therefore, it is also possible to simulate something that is not possible in the real physical word, but it would lead to unique and interesting sounds!
Even just doing tests to see if our physical modeled instruments really sound like a physical (real) version is a great motivation to explore this topic. This also leads to a better understanding of the instrument itself.
This also opens up the possibility of playing instruments with slowly changing parameters. We could also do a real Morphing between instruments, not only in the studio, but also during a live performance. Obviously this will lose the realistic part of the instrument itself, but it could work perfectly for an experimental performance (and not only).
What exactly is modeled?
Real instruments are “broken down” into their components such as string, sounding board, tube, mouthpiece, hammer and so on, in order to model them all separately.
It is also important to add some non-linear components (such as diodes, transistors, inductors and iron core transformers), as most tools contain them, but they are really difficult to manage analytically. A bit of randomness is also a really important part, as if we had total control of all parameters, we would lose the reality of the instrument. (there is always a small percentage of randomness in the real word!)
This is the first commercial physical modelled synthesizer (1994), it calculates model of wood instruments:
Sample oder Physical Modelling?
Here are some other examples (VST):
Based on physically modeled acoustic resonators
Wikipedia – Physical Modelling
Physical Modelling – Seminar Klanganalyse und Synthese, TU-Berlin, 2001