At t=0 when the impulse occurs there are no reflections, they propagate at the speed of sound and it takes some time for them to reach a steady state, probably infinite time for an infinite array. Initially, an observation point in the middle close to the source would receive wavefront rays from nearby source points first. As time goes by reflections from points more near the boundary planes would reach the point. Assuming angle of reflection is mirror of angle of incidence, some reflection rays would be almost perpendicular to boundary surfaces and arrive at the very-near-to-source-observation point after the first bounce, most would miss it, some would hit on the second bounce. etc., etc.
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And your point is?
Actually if the line source goes up to the reflecting surfaces then there is an immediate reflection from that part, no delay and there is no "steady state" with an impulse.
The time-domain impulse response for an Infinite Line Source was developed in this thread (POST #19a, in its simplest form). All of it, every bit of it, from t=0 until the end of time. Later, a "qualitative description" of that impulse response shape and behavior was offered (POST #20).
It's IDENTICAL to the time-domain impulse response from a Finite Line extending between two perfectly reflecting surfaces.
Finally, as Earl said, there is no "steady state" behavior to the impulse response.
By delay, I was referring the time it takes for a wave to travel at the speed of sound, propagation delay. It's not instantaneous.
Regarding steady state, see the first example here on page 2: https://www.maplesoft.com/content/EngineeringFundamentals/50/MapleDocument_48/Transient_Respons.pdf
It says:
"A long time after the switch is opened and the capacitor has discharged, the system will again reach a steady state. The voltage remains constant at zero, and the current is also zero because of the constant voltage across the capacitor."
Steady state can be zero volts at infinity time.
Anyway, what I was trying to get at is that if at t=0 you have a gazzllion little men in a vertical line all set off starter pistols, and you are interested in the sound arriving at some particular point adjacent to the line, the sound from the infinite number of starter pistols will arrive at your location after a delay associated with the distance away each one is. In other words, I am trying to paint a physical picture for people in the forum who are more comfortable with mechanical intuitions than equations. So, the question is how do you explain why there is a tail in the English language rather than in mathematical language? More often than not, its possible to explain something if the physical process is fully understood. It is possible for people to learn how to work equations, but not truly understand what is happening physically (not understand well enough to teach it).
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Already done, earlier in this thread. I've not only developed the math, but ALSO qualitative descriptions (with no equations).
Please read POST #20 (#191 on page 20)
(see also, the end of POST #17, which is #168 on page 17)
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Lower distortion and power compression when each driver will have to work "less hard" for a given SPL or what ?
What about impedance is there any chance a higher impedance string can evolve small bit of higher dynamic range than a lower impedance string of drivers ?
YES, if there's one thing i've emphasized over and over in this thread ... the frequency response and impulse response, are mathematically linked. Even stronger ... for all intents and purposes, they are the exact same thing. Tell me one of them, and i'll tell you the other. If the frequency response isn't flat, then the impulse response is NOT, itself, an impulse.
An analogy : If you give me a number (providing it's not too big), i'll tell you the prime factors of that number. Or, if you give me the prime factors, i'll tell you the number. It's a unique relationship, that allows for no ambiguity or "wiggle room".
So it is, with frequency response (magnitude and phase), and time-domain impulse response. They are "transform pairs", with a unique, non-ambiguous relationship
In the world of audio, it often makes more sense to "look" in the frequency domain, rather than the time domain, simply because of properties of human hearing. For example, human hearing is bandlimited to about 20Hz to 20kHz, and is very sensitive to magnitude over that range while being very insensitive to phase over that range. It's much harder to determine bandlimited, magnitude-only content in the time domain
so, we look at the frequency domain instead. Of course, there's that other wonderful property (discussed very early in this thread) that convolution in the time-domain, becomes simple multiplication in the frequency domain ... which makes operations (like filtering) MUCH easier to understand For ALL of these reasons, we tend to spend more time ... especially in audio ... in the frequency domain, instead of the time domain. Both domains contain the EXACT same information, because they are uniquely linked, but the info we care about is just more readily "visible" in one of the domains.
The linking of course assumes we are working with a linear system. Hearing is in some ways nonlinear primarily because of how the brain processes nerve impulses from the ear. Brains use something like neural phase lock loops for some things like frequency perception. But time domain perception for lateral sound source location estimation operates on a faster time scale than would correspond to the maximum frequency that can be heard. There are other examples of hearing perception being very dependent on factors that operate in ways very unlike our engineered systems.
That depends a lot on the details of the specific drivers being used doesn't it? It is not going to be true in general, even if it is true is some cases. It takes a lot of small sources to equal the capabilities of one 15" high efficiency driver. My point sources have enough dynamic range that audible nonlinear distortion is not a factor so what difference does it make if something else is greater?
Your second question is not clear to me, but I don't see any connection between dynamic range and impedance.
Somewhat true, but not exactly.
Hearing is nonlinear, but not because of the brain, but because of the physical system of the hair cells. The hair cells themselves have the phase lock loops that extend our dynamic range to the extent that it has. The hair cell neurons themselves only have about 60 dB of dynamic range, but our hearing is about 120 dB. The extra 60 dB comes from this phase lock loop amplifying the signal at specific input frequencies.
Perception of all sounds operate at every higher speeds - shorter time scales - as the frequency goes up simply because the GammaTone filters that are analogs of how our hearing works have ever shorter impulse responses that respond more quickly.
More recent research shows more going on in the brain that was previously understood, such as perfect pitch perception, an ability which is believed to form in the brain with greater probability when infants are exposed to singing and music at a very early age. Brain neuroplasticity also accounts for how language is learned, and for the brain's ability to pick out threatening words buried in noise from a known language, more so than its ability to extract unfamiliar signals from noise. Another example might be ear training that music majors receive where they learn to hear masked notes in chords in order to perform transcription. Or, how about the well known example of not being able to hear a cough occurring in the middle of a spoken word. The word is heard as being without interruption and the cough is heard as occurring between words.
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So you are saying that the sensitivity of a line array is greater than a point source? If so, then that isn't always true either. It depends.
I know that line arrays have a strong following and I am sure that there are some very good ones out there, although I haven't heard any. My point would be that there is no inherent basis for superiority of either the line source or the point source. It's all about implementation. I honestly suspect that as both types got better and better that they would begin to sound the same.
It seems to me that implementing constant directivity in the horizontal plane from a line source would be very very difficult. To me, this is a strong negative as most research has shown a preference for constant directivity.
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This is true, that is a brain function that has to be developed. (But this is different than what you were claiming before.)
It is no coincidence that perfect pitch is almost universal for people who live with languages that are tonal, like Chinese. One has to learn to differentiate pitch from the earliest ages when learning this language. For those of us in a syllabic language, we are taught to mostly ignore the pitch, because it does not convey any information - it is accent. Hence perfect pitch is rare in those countries.
Dependence specific used devices sounds right, second question was because in past never got to ask a French member who commented 4 ohms is for car use, take 16 ohms or 8 ohms he said and wondered ever since if higher impedance could evolve bit higher dynamic range or other reason can think of is relative better relation of damping to a modern low impedance amp could be what he was after, anyway thanks.
Yes. Really the thing that concerns me a little and than I would like to see change is that many engineers are so used to thinking in terms of linear systems and linear models that it seems like there is some tendency to assume that hearing is more linear than it actually is. Most probably don't need to become experts, it's just something to keep in mind. Also, the old psychoacoustics books contain a lot of useful information, but aren't fully up to date. Some of the more recent publications are in the areas of cognitive psychology, musicology, and medical research related to hearing aid technology.
Couple points :
- One must THOROUGHLY understand linear systems, before one can even begin to understand non-linear systems. In fact, the approach to modeling and understanding "non-linear" mechanisms is, quite often, to "linearize" them (small-signal analysis, describing functions, etc).
- All too often, i've seen (heard?) very esoteric, non-linear mechanisms be "blamed" for audible consequences of simple, linear phenomenon. Best advice is to "rule-out" the basic linear mechanisms first, before complex non-linear causes/issues are invoked
Werewolf
This is so true. Take diffraction for example. It becomes more audible with SPL, i.e. it sounds nonlinear like THD, but it is a linear phenomena, its just that our ear/brain has a nonlinear perception of it.
And if you don;t completely understand linear systems you will never understand nonlinear ones.
This is so true. Take diffraction for example. It becomes more audible with SPL, i.e. it sounds nonlinear like THD, but it is a linear phenomena, its just that our ear/brain has a nonlinear perception of it.
And if you don;t completely understand linear systems you will never understand nonlinear ones.
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