Physical Modeling

Physical modeling

Sound happens whenever something vibrates at audio rate. The aim of physical modeling is to reproduce those movements that happen in real world instruments by creating self oscillating systems.

Of course some instruments are simpler to figure out and to model than others. A cymbal which appears to be only a piece of metal you hit on is a PITA to model, whereas a guitar string is probably the simplest thing.

Modeling a plucked string

You can consider a string as a short bidirectional loop.

Figure A :

So, you could model it with only one delay with feedback path. 2 delays will let you capture sound in both directions. And don’t forget to invert the signal after each delay.

Pitch depends on the delay time. The shorter the time, the higher the pitch. cf Karplus-Strong algorithm : http://en.wikipedia.org/wiki/Karplus-Strong_string_synthesis

Modeling a reed

Another simple model is the reed. You can find a reed in a lot of instruments. The mouthpiece of a recorder uses quite a similar logic to that of the reed, but it does so by making the air coming from the mouthpiece go alternatively out the first hole or into the bore, depending on the pressure. The simplest reed instrument is probably the harmonica.

Here are the bases for an oscillation that should sound like a reed:

Figure B :

Figure C :

If you are interested in physical modeling, don’t miss this address:

http://hyperphysics.phy-astr.gsu.edu/hbase/music/musinscon.html#c1