I've never studied physics so I can't give an answer in mathematical form. I can't even guarantee this is all perfectly correct but I'm pretty sure it is. I'm going to avoid talking about pressure and velocity since I'm sure to make mistakes that way, I'll just talk about flow.
Let's start here - a garden hose of incredible length, let's say 1 mile long. If the garden hose is empty (full of air) and you turn the water on there is a delay before water starts to come out the end of the hose. BUT if the hose has already been used and is full of water, the instant you turn on the water it starts to come out the other end.
That's how a front loaded horn works, it contains a slug of air and it's always full of that slug of air so flow at the mouth is instantaneous. As soon as the cone moves the air at the mouth is also forced to move. Immediately. Pushing in on the throat causes air to come out the mouth.
A tapped horn works the same way. But since there is an extra source of sound (the mouth side tap) there is a complex interaction between the two sources. Both of the sources still operate in the same fashion (the same as a front loaded horn - pushing in on the throat causes immediate flow out the mouth) but now there are two very distinct sources and those two sources cause very distinct behavior at different frequencies because their position has different effects on impedance.
Below is a pic showing:
1. response of a tapped horn (it's actually a tapped straight pipe since I didn't want to spend too much time on this)
2. response of the throat side tap alone
3. response of the mouth side tap alone
As you can see, the throat side tap is the side that gets all the work done. The mouth side tap only contributes very sharp and narrow spikes. If the tapped horn is designed well, one of those spikes will fill in a natural transmission line null and you will get flat(ish) response over as much as 3 octaves - the rest of the mouth side tap response spikes are not useful and may even cause problems. Without the mouth side tap there will always be a big tl null somewhere in the middle - until the design gets large enough to be a true horn and not a transmission line.
Anyway, the point is that both taps work the same but they have very different behavior depending on frequency because of their position and that position's effect on impedance. Impedance is a very major player here and it causes vastly different things to happen at different frequencies due to the tap position, hence the massive phase shifts with tapped horns.
Imagine this - no matter which way the cone is going, it's going to be exhibiting positive pressure on the throat at some frequency, depending on tap position (which tap is dominant due to impedance).
If this doesn't help I'm not sure I can explain it more clearly.
Let's start here - a garden hose of incredible length, let's say 1 mile long. If the garden hose is empty (full of air) and you turn the water on there is a delay before water starts to come out the end of the hose. BUT if the hose has already been used and is full of water, the instant you turn on the water it starts to come out the other end.
That's how a front loaded horn works, it contains a slug of air and it's always full of that slug of air so flow at the mouth is instantaneous. As soon as the cone moves the air at the mouth is also forced to move. Immediately. Pushing in on the throat causes air to come out the mouth.
A tapped horn works the same way. But since there is an extra source of sound (the mouth side tap) there is a complex interaction between the two sources. Both of the sources still operate in the same fashion (the same as a front loaded horn - pushing in on the throat causes immediate flow out the mouth) but now there are two very distinct sources and those two sources cause very distinct behavior at different frequencies because their position has different effects on impedance.
Below is a pic showing:
1. response of a tapped horn (it's actually a tapped straight pipe since I didn't want to spend too much time on this)
2. response of the throat side tap alone
3. response of the mouth side tap alone
An externally hosted image should be here but it was not working when we last tested it.
As you can see, the throat side tap is the side that gets all the work done. The mouth side tap only contributes very sharp and narrow spikes. If the tapped horn is designed well, one of those spikes will fill in a natural transmission line null and you will get flat(ish) response over as much as 3 octaves - the rest of the mouth side tap response spikes are not useful and may even cause problems. Without the mouth side tap there will always be a big tl null somewhere in the middle - until the design gets large enough to be a true horn and not a transmission line.
Anyway, the point is that both taps work the same but they have very different behavior depending on frequency because of their position and that position's effect on impedance. Impedance is a very major player here and it causes vastly different things to happen at different frequencies due to the tap position, hence the massive phase shifts with tapped horns.
Imagine this - no matter which way the cone is going, it's going to be exhibiting positive pressure on the throat at some frequency, depending on tap position (which tap is dominant due to impedance).
If this doesn't help I'm not sure I can explain it more clearly.
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The sound waves move through the "slug of air" at the speed of sound (about 1130 feet per second, just as in the empty garden hose), not instantaneously. The speed of sound in water is more than four times that in air, but still is not instantaneous.
The mile long garden hose example is hydraulic, not acoustic.
If the slug of air moved instantaneously, we would not have to delay top cabinets to align with the horn loaded bass cabinet's acoustic center.
Just as in a front loaded horn, the TH needs to have the top cabinets delayed to coincide with the "time of flight" determined by the horn's path length.
To address this specifically, I think you are forgetting about impedance. Impedance changes everything. If there was no impedance there would be no (or very little) flow out the mouth at all. The air would just circulate back and forth between the throat side tap and the mouth side tap and very little else would happen, same as a driver in free air (which only has external impedance based on it's cone size and therefore can only play convincingly above the baffle step frequency dictated by this size).
Your very simple physics is a bit too simple here, it doesn't account for impedance.
Sure, you are correct as usual. The point I was trying to make here is that there isn't a long delay (as there would be if the garden hose was full of air). Neither tap is more "connected" or "faster" than the other. The only reason one is more influential than the other at any given frequency is impedance.
The original question asked why there wasn't low pressure at the mouth first when the cone moves into the throat, since the mouth side tap is closer why doesn't it create a low pressure?
I suppose I could have left out the garden hose and toothpaste analogies entirely since the answer is simply impedance. But impedance can be hard to visualize.
Anyway, do you see any other problems with what I said? I really struggled to put it into words, I hope it's mostly ok.
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I think your focus on impedance is missing the basic reason the TH works, which was nicely explained by Tom Danley in his White Paper on TH technology:
"Since the rear of the driver is much closer to the mouth of the horn, at very low frequencies it is effectively de-coupled from the system and its radiation does not affect the total output. This occurs due to the throat end being almost one-quarter wavelength away. The radiated pressure from the rear of the driver is reflected from the throat end back toward the mouth. The total path length traveled is one-half wavelength (one-quarter down & one-quarter back). The reflected wave arrives 180° out of phase with the original radiated pressure from the rear of the driver and is thus cancelled.
As frequency increases the situation changes a bit and the rear of the driver begins to be coupled to the horn as the reflection from the throat end does not cancel its own radiation. When the frequency is such that the horn is one-half wavelength long the rear of the driver is fully coupled to the horn. The pressure from the front and rear of the driver are of reverse polarity; a 180° phase shift at all frequencies. The pressure from the front of the driver (at the throat) and the pressure from the rear of the driver (close to the mouth) are now approximately one-half wavelength apart. This represents a phase shift of 180°. At this frequency both the front and rear of the driver are driving the horn in phase. When this happens the driver’s radiating surface area (Sd), as far is the horn is concerned, had significantly increased (almost doubled). Since the driver radiates from the front and back of the diaphragm, this yields very different driver parameters than when at the one-quarter wavelength resonance condition."
Like in comedy, timing is everything
..Art
Yeah, but like most of Danley's quotes, this one is diluted to the point of being only true in a broad sense, he likes to reveal a sense of how something works but not the details. It is true that the front and back tap are 180 degrees out of phase based on the fact that one side pushes while the other side pulls. But like I said in post 61 there is a complex interaction between the two sources, it's not quite as simple as Danley's quote would lead you to believe.
The output of the mouth side tap is not simply decoupled at low frequencies and coupled at high frequencies. The output at all frequencies is summed based on impedance and phase, and since phase is all over the place (above and below zero degrees) it adds at some frequencies and subtracts at some frequencies.
Since the phase responses of the front and rear tap in the previous example look something like this:
The sum of impedance and phase is very complex indeed. Not at all simple as decoupled at low frequency and coupled at high frequency.
Now this is all quite a ways outside my comfort zone, I don't know the underlying math and I can't draw a frequency response curve based on summation of impedance and phase of two separate sources without a computer to do the heavy lifting, but I assume if you ask Mr McBean, he will say that the tapped horn computations are done by summing impedance wrt phase of the two separate sources inside the line and the results are not as simple as Danley's quote suggests. At some frequencies it works the way he says it does but it's not nearly that simple.
It's clearly not as simple as I've tried to describe it either (with analogies) but it is true that the only purpose of a tapped horn (as opposed to an untapped transmission line of the same design but without the mouth side tap) is to fill in a naturally occuring transmission line null.
The output of the mouth side tap is not simply decoupled at low frequencies and coupled at high frequencies. The output at all frequencies is summed based on impedance and phase, and since phase is all over the place (above and below zero degrees) it adds at some frequencies and subtracts at some frequencies.
Since the phase responses of the front and rear tap in the previous example look something like this:
An externally hosted image should be here but it was not working when we last tested it.
The sum of impedance and phase is very complex indeed. Not at all simple as decoupled at low frequency and coupled at high frequency.
Now this is all quite a ways outside my comfort zone, I don't know the underlying math and I can't draw a frequency response curve based on summation of impedance and phase of two separate sources without a computer to do the heavy lifting, but I assume if you ask Mr McBean, he will say that the tapped horn computations are done by summing impedance wrt phase of the two separate sources inside the line and the results are not as simple as Danley's quote suggests. At some frequencies it works the way he says it does but it's not nearly that simple.
It's clearly not as simple as I've tried to describe it either (with analogies) but it is true that the only purpose of a tapped horn (as opposed to an untapped transmission line of the same design but without the mouth side tap) is to fill in a naturally occuring transmission line null.
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Here's one more note on this point and maybe it will help to clarify the role of the mouth side tap. Especially in the beginning (when tapped horns were first introduced) and even recently I've seen people talking about how tapped horns are twice as loud as an equivalent untapped design because both sides of the cone radiate into the horn. This isn't how it works.
Here's a pic showing the previous example but I moved both taps to the ends of the line as far as they would go - 0.01 cm from either end.
Pic 1 shows the schematic of this tapped horn.
Pic 2 shows the same thing except I removed the mouth side tap completely - so it's just an end loaded tl.
Pic 3 shows the response of each overlayed.
An externally hosted image should be here but it was not working when we last tested it.
As you can see in graph 3, the mouth side tap is doing absolutely nothing. Above 100 hz there are some minor changes but nothing that would actually be measurable. Moving through all the Hornresp windows, all the different graphs overlay just as well - acoustic and electric impedance, displacement, phase all overlay almost perfectly. There is a bit of difference in group delay above 500 hz but that hardly matters.
This is just a theoretical example since afaik you can't physically build a tapped horn with the taps so close to the ends of the line but IMO this is a useful example to show the nature of what the mouth side tap really does. At most frequencies it isn't doing much of anything but if the tapped horn is designed just right so the mouth side tap is in the right spot, it can be used to fill in a specific hole in response that naturally occurs in transmission lines.
This is also the reason that air can flow out the mouth when the cone moves in towards the throat. At frequencies where the throat side tap is dominant, the mouth side tap is simply not doing much - it's acting like an untapped tl for the most part.
Hi Chris,
You are quite correct.
The attached screenprint shows the impulse response for a three-segment tapped horn with L23 = 344 cm. The initial negative spike (amplitude -0.5) is generated by the rear side of the driver near the horn mouth, and the later large positive spike (amplitude +0.9) is generated by the front side of the driver near the horn throat. As expected from the theory, the delay between the two spikes is 10 msec.
Delay = L23 / c = 3.44 / 344 * 1000 = 10 msec.
Kind regards
David
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Acoustic impedance, or electrical?
The situation you describe does occur, at frequencies below the lowest tuning of the TH: the wavelengths are long enough that the pressure wave has made it round to the other side of the driver while it hasn't moved much from the position that created that pressure wave. High pressure meets low pressure and the two cancel, which is why excursion goes bonkers below lowest tuning.
So far as I can tell, the phenomenon above is a function of wavelength and path length. Impedance (acoustic or otherwise) doesn't come into it.
David, thanks for your response. It hadn't occurred to me to run an impulse simulation. I'll have a play around and see what can be found.
Cheers
Chris
Again, I'm a bit out of my comfort zone here, I don't spend a lot of time looking at and comparing impulse graphs. So I took some time to do just that.
An externally hosted image should be here but it was not working when we last tested it.
That's 3 different designs shown with and without a mouth side tap. Each shown as a schematic with the resulting impulse behavior beside it.
Design 1 is the one I've been using here previously.
Design 2 is a popular diy design. (Shown mainly because I found something weird with this one.
Design 3 is the same as #2 but 8x larger and with 8x more drivers.
First note - up until the first really large positive spike (the second positive spike in each case) the impulse response looks very much alike whether there is a mouth side tap or not. Compare the two different (tapped and untapped) results of each design and the impulse response isn't perfectly identical but it is very very close.
The only way I could get an initial positive spike (instead of an initial negative spike) was to show only the line response. As soon as you show the combined response (line and driver combined) with any of the non tapped designs, the impulse has the same shape as the tapped equivalent.
Second note - impulse start times are confusing to me. In design 1 (both tapped and untapped) impulse starts at 0. In design 2 the tapped impulse starts at around -10 but the non tapped impulse starts at 0. In design 3 both the tapped and non tapped impulses start at around -10. This seems weird, maybe I just need to study a bit more about what the impulse is trying to tell me but I'd appreciate an explanation if you have one.
Anyway, disregarding impulse start times, the shape of the impulse graphs (positive vs negative) seems to be the same regardless of whether a line is tapped or not. So the initial negative spike does not seem to be generated by the rear side of the driver by the horn mouth as you said in this quote, since this behavior is also seen in non tapped lines as well.
To make this as simple as possible, all I'm trying to say is that the vast majority of the time (at most frequencies) a tapped horn is operating very much like an untapped transmission line.
That's not to say that there's not a complex interaction between the taps going on at all frequencies, but most of the time the throat side tap is dominant and the line acts very similar to it's untapped equivalent.
Hopefully I can answer some of my own questions here. First -
That answers all my questions about timing. (From Hornresp Help)
And a picture.
Pic 1 - combined impulse response (both driver and line impulse together)
Pic 2 - impulse from horn mouth alone (no driver impulse)
Pic 3 - combined response at +500 cm distance (at horn mouth - notice similarity to graph above)
Pic 4 - combined response at -500 cm distance (at driver)
Pic 5 - schematic of the 500 cm end loaded tl being simulated
This is an end loaded tl (not a tapped horn) and it's combined impulse response starts with a negative spike. Summing graphs 3 (horn mouth impulse) and 4 (driver impulse) results in the combined impulse shown in graph 1. (Driver impulse precedes mouth impulse in graph 1 by a few ms since the rear source is buried in the tl, which adds a few feet of path length delay).
So it can be seen that even regular transmission lines start with a negative impulse spike and it comes from the driver, it's got nothing to do with whether the line is tapped or not. (As far as I can tell.)
That answers all my questions about timing. (From Hornresp Help)
And a picture.
An externally hosted image should be here but it was not working when we last tested it.
Pic 1 - combined impulse response (both driver and line impulse together)
Pic 2 - impulse from horn mouth alone (no driver impulse)
Pic 3 - combined response at +500 cm distance (at horn mouth - notice similarity to graph above)
Pic 4 - combined response at -500 cm distance (at driver)
Pic 5 - schematic of the 500 cm end loaded tl being simulated
This is an end loaded tl (not a tapped horn) and it's combined impulse response starts with a negative spike. Summing graphs 3 (horn mouth impulse) and 4 (driver impulse) results in the combined impulse shown in graph 1. (Driver impulse precedes mouth impulse in graph 1 by a few ms since the rear source is buried in the tl, which adds a few feet of path length delay).
So it can be seen that even regular transmission lines start with a negative impulse spike and it comes from the driver, it's got nothing to do with whether the line is tapped or not. (As far as I can tell.)
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Hi
No It's positive for an Nd or OD Loaded Quarter-Wave pipe/tube but (normally) due to the Driver front orientation(Changing TH to Nd or Od) is facing the throat for an TH in HR a positive stroke result in a negative rarefaction-wave that is first propagated towards the listener ( Equal distance to the terminus and the Driver is assumed ), i.e. the IR shows a negative impulse as seen in the plot.
b
Hi
No It's positive for an Nd or OD Loaded Quarter-Wave pipe/tube but (normally) due to the Driver front orientation(Changing TH to Nd or Od) is facing the throat for an TH in HR a positive stroke result in a negative rarefaction-wave that is first propagated towards the listener ( Equal distance to the terminus and the Driver is assumed ), i.e. the IR shows a negative impulse as seen in the plot.
b
I'm not sure what you are talking about, the driver is always facing the same way. Look at the pics in post 71. In each case (regardless if the line is tapped or not) the impulse always has the same shape, it always starts with a negative spike from the driver and a few ms later you get a positive spike from the mouth. The pics in post 74 show how the driver impulse and the mouth impulse add up. There's a strong negative spike from the driver and then a few ms later a strong positive spike from the mouth.
If you only look at the output from the mouth of an untapped tl then the impulse starts with a positive spike.
If you are trying to say that if you reversed the polarity of the driver and started with a positive spike from the driver then a few ms later you would see a negative spike at the mouth, then I agree with you. But that would be consistent with both tapped and untapped transmission lines. They both work the same way in this regard.
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When measured in the reality: A typical TL do not have a negative onset IR slope. HR turns it upside down thus do not depict the 'IR' reality for 99...% of a TL build when in TH screen mode or in OD mode or in 'Nd' too.
As said before this is not what you normally expect for a typical mounted Driver...
Your reversed polarity is bought from HR and is valid within this program for a TH or a FLH. The reference for a speaker Driver with a positive applied voltage results normally in a positive cone displacement, i.e. in a positive spike and as almost 100% of all TL design have the Driver front visible.... a positive spike is expected at first in a plot or measurement.
IMO, If you want to model a Nd TL with a correctly depicted IR: The only way to do this is to use the same input screen as for a Ported BR-box and use Ap1 +Lpt to adjust the length and CSA. A Normal OD-TL doesn't work.
The plot in the submitted picture marked with a Red Astrix is an expected IR if you measure at the terminus of a TL.
b
PS: A TL have no Mouth but a Terminus or a Port thus in reality the IR for a stuffed TL cannot have a 'spiky' onset response from the Terminus/Port side due to the BW restriction, thus the first sound energy to reach a listener is always originating from the front-side of the cone when the Terminus/Port and Driver are equidistant to a listener.
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Hi just a guy,
For the purposes of calculating impulse response, Hornresp assumes the convention that the side of the driver diaphragm facing the horn throat moves towards the throat, thus increasing the instantaneous pressure on the throat side. This is why the initial spike is negative for both tapped horns and the combined response of an offset driver horn.
Rest assured, the initial negative spike shown in my tapped horn impulse response example is definitely being generated by the side of the driver diaphragm facing the horn mouth
.Kind regards,
David
I hate to resurrect this notion since this talking point seems to have had it's chance already, but just for my own clarification...
When we're talking about the physics of the air inside a tapped horn, are we absolutely sure we should be talking about the speed of sound? We know that sound, or more accurately, ripples move through air at a particular speed, but inside a trapped air volume, where the driver movement actually changes the volume (displaces) air that's inside the cabinet, is it still really just "shaking" the air?
When I imagine what happens in my head, it seems that there should be some measure of the "air slug" being pushed as a mass, similar to how air works in an air actuator...if you open the valve going from an air compressor to an air piston device (like we've seen mythbusters do when making air powered punching fists and such), you don't need to wait for the speed of sound to see it actuate..
Or do you?
Edit: I realize that when the cone moves positively, the increase in volume on the mouth side from having the cone move in gives a reciprocal space for the air to be, but I'm still trying to wrap my head around how the speed of sound plays much of a part in all this until the barrier where the mouth interacts with open air after the mouth.
When we're talking about the physics of the air inside a tapped horn, are we absolutely sure we should be talking about the speed of sound? We know that sound, or more accurately, ripples move through air at a particular speed, but inside a trapped air volume, where the driver movement actually changes the volume (displaces) air that's inside the cabinet, is it still really just "shaking" the air?
When I imagine what happens in my head, it seems that there should be some measure of the "air slug" being pushed as a mass, similar to how air works in an air actuator...if you open the valve going from an air compressor to an air piston device (like we've seen mythbusters do when making air powered punching fists and such), you don't need to wait for the speed of sound to see it actuate..
Or do you?
Edit: I realize that when the cone moves positively, the increase in volume on the mouth side from having the cone move in gives a reciprocal space for the air to be, but I'm still trying to wrap my head around how the speed of sound plays much of a part in all this until the barrier where the mouth interacts with open air after the mouth.
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the slug moving effect is only for VLF.
At audio frequencies the air compresses adjacent to the cone and this compression travels as a ripple at the speed of sound from the moving cone around the route from throat to mouth.
It's that speed of sound time of travel that creates the time difference between the direct to mouth pulse and the throat generated pulse.
At audio frequencies the air compresses adjacent to the cone and this compression travels as a ripple at the speed of sound from the moving cone around the route from throat to mouth.
It's that speed of sound time of travel that creates the time difference between the direct to mouth pulse and the throat generated pulse.
Hm, so, if I were to construct a tube with a moving plunger and a handle at one end and another plunger at the other (similar to a hypodermic needle, but with two plungers) and oscillated one, at say, 40 cycles, the slave plunger would slip out of phase with the one that was being oscillated, shifting more and more out of phase directly related to the distance apart / speed of sound?
Edit2: Assuming there is zero drag on the plungers and their mass is also zero.
I guess in my brain air movement works differently inside a sealed pressure vessel than it does in open atmosphere..maybe I'm just ill-read on the subject
Edit: I realize the visual of a man trying to manually oscillate a handle at 40 cycles is quite amusing.
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