Putting the Science Back into Loudspeakers

[DBMandrake]

It is never possible to dampen resonances entirely without effecting the forced response. This is the part that gets tricky. Therefore, during measurements it is necessary to look at both forces and natural response to help make the design balance. Of course distortion needs to be looked at too depending on material used.

The air in the room moved by a speaker doesn't know what is forced response and what isn't. You're drawing an artificial distinction here.

The resulting impulse response representing the amplitude and phase response of the speaker is all that matters here. It doesn't matter how much of that is a direct result of forced response and how much is factors like unforced mechanical resonances.

If you have a mechanical resonance (unforced movement) and you then precisely correct for that with active EQ the impulse/amplitude/phase response now matches the intended forced response exactly. Where is your unforced resonance now ? For all intents and purposes it does not exist. The poles and zeros have canceled each other out.

If it looks like a duck, walks like a duck, quacks like a duck..... ?

In short forced vs unforced is simply an implementation detail in achieving the final impulse response.

 

[soongsc]

This is why CSD is a good way to understand the natural response of a system. Although it may not associate exactly, you know whenever you look at the CSD response if you are in the right direction of a driver design.
If you are not into tweaking drivers or designing drivers, you may or may not see the difference.
SoundEasy recently implemented a CSD difference function which is quite convenient to help in the process.

 

[gedlee]

In short forced vs unforced is simply an implementation detail in achieving the final impulse response.

I don't quite like your terminology, although I agree with what you are trying to say. I think that you should talk about the forced response versus the natural response - those are the proper mathematical terms. If something is "unforced" then it doesn't have any response. Objects can't respond to something that isn't there.