OWC
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The step response or impulse response (same thing) is literally the same as a frequency response, just a different representation.have you look on this page with the desktop web browser and not with mobile ?. there can comment or edit the page same way as in wiki. BTW: I have not create or edit this page. on this page stand too that step response show time. and the frequency a speaker can reach depend on the rise and fall time and the linearity of this. step repsonse is also important measure for hydraulic systems. for hydraulic systems there is no frequency diagram show
Practically speaking a step is a little difficult on a loudspeaker, unless you would like to first put a lot of DC on it and quickly switch it off.
Which I wouldn't recommend doing and is also not always possible with a capacitor in series.
So therefor we use impulse responses, but with some math they are interchangeable.
I have a background in physics, so I used to work with quite some hydraulic systems in the past (good old control theory systems)
The thing is, a frequency response just simply doesn't make sense for such a system, since it's not a point of interest.
An hydraulic system would also never work like a speaker on many frequencies, but just one impulse.
So in the end engineers are only interested in response times as well as how much shoot through there is (= Q factor).
There is no ideal step response for such systems, and by definition it's always a trade off between how fast you wanna switch things off, vs how smooth. With the disadvantage that a very "fast" system will shoot through and a very slow system will take forever to close a certain valve (or what have you)
For a slower system in sense of mass, the frequency response would just simply collapse, which is the same as a low pass filter.
Unless you mean the low frequency side of things, in that case an higher Q will just result in a peak (like said above) or have a very shallow output around the Fs (for Q < 0.707). Also the amount as well as the shape of the group-delay changes.
I find it a little strange to call that linearity, unless you call any kind of frequency dip or peak linearity as well?
In this case engineers don't really care about velocities or acceleration, but rather are interested in cone excursion vs max bandwidth (or peaks) vs lowest -3dB pont vs smooth crossover with roomgain vs a group delay that doesn't jump all over the place (sudden changes in GD can be audible).
So there is a trade-off again, although a good system should be between 0.5 < Q < 0.707
Much lower just doesn't makes any sense anymore and you will loose heaps of output, above 0,707 will give a peak in de frequency response.
Anyway, I don't really see the link between phase response and a certain impulse/step response.
Since there are many other things changing with the Q-factor as well.
The difference in group delay is also very small in practice.
Personal side note, is that I very often wonder what companies had in mind?
Looking at certain frequency responses and the lower-end looks totally awful, with sometimes an huge peak around the Fs = high Q factor.
I still find it a little strange that Toole never said anything about it in his books.
Because that is definitely audible unless room modes are far more substantial.