psb_87 wrote:But the thing is, (and this is a MASSIVE oversimplification) not much LF energy can actually get through a relatively small opening, such as a duct. This is due to a large impedance mismatch - the large body of air of the room and the small hole of the duct.
That's a common misconception, actually. Yes, there is an impedance mismatch, and therefore there is some loss, but the effect is nowhere near as big as some people imagine. It's only a few dB at best. Also, it is not related to the
volume of air in the duct and the
volume of air in the room, but rather to the
cross-sectional area of the duct vs. the effective
cross-sectional area of the room surface where the duct penetrates.
Here's a graph from Engineering Acoustics that shows the real effect:
So for example, if you have a 10" duct going through a wall that is 8 feet high and 8 feet long, that means you have a bit more than 2 square feet going into 64 square feet, which is a ratio of 32 to 1. According to the graph, that would give you about 9 dB insertion loss.... interesting, but not exactly spectacular! Assuming that your duct is coming from the tracking room, where some gorilla band is thrashing the drums, bass, keyboards, and screaming electric guitar at 120 dB, and that you were getting mathematically perfect attenuation on BOTH ends of the duct, there would be an 18 dB drop (9 dB on each end). So George the Gorilla Group would still be smashing out 102 dB on the other send of the duct...
If you are interested in the actual equation, it goes like this:
dL = 10 log( ( 1 + A1 / A2 )2 / 4 (A1 / A2) )
where
dL = noise attenuation (dB)
A1 = inlet area (m2)
A2 = outlet area (m2)
There's another massive caveat to the above graph and equation: it is the
best-case scenario! And it assumes a sudden, sharp change in cross-sectional area, with the duct hole in the exact center of the wall, both vertically and horizontally. Of course in real-life rooms, the duct is never in the middle of the wall, so you can only calculate the area to the closest intersecting surface (ceiling/floor/other wall), and the transition is never sharp and sudden: it pretty much always goes through a register of some sort. So the actual insertion loss is considerably less.
For a real-world scenario, assume that the duct comes in one foot below the ceiling and one foot away from an intersecting wall, so you can only consider a cross-section of about 10 square feet wall area vs. 2 square feet for the duct, so the actual ratio is about 5:1.... which would give you a 3 dB drop (being very generous!). Add a register into that, and even if it has really low-loss vanes and 70% open area, your actual losses are down to just 1 or 2 dB.... with luck.
This is why silencer boxes are designed with at least two sudden changes in cross section of at least 200% to 400% or so, as part of the many, many tricks that go on inside, and that gets you a couple of extra dB insertion loss. That's all. In a well-designed silencer box, there's also things like right-angle turns, sudden changes in airflow, tuning, baffles, porous absorption, mass, and a few other nifty bits. All of that, in total, can get you very decent insertion loss. A pair of boxes (one on each leaf, coupled with flex duct), can indeed get you a total TL greater than the TL of the MSM wall itself: commonly of the order of 50 dB, or more where needed.
If an acoustic flex duct is connected to the hole then the LF transmission is basically negligible.
Well, no, I would not agree with that. Just listening to such a duct coming through the wall of a drum booth will probably convince you that the losses are considerably lower than you imagine, and plenty of sound still gets through.
and the attenuation improves with distance.
Yes, at the normal rate of 3 dB loss for ever distance doubling, assuming we are talking about open air (not restricted by boundaries, such as walls and a ceiling).
Now, that's not to say that you shouldn't worry about holes, or air tightness - you still want to have a completely air tight enclosure and seal and gaps and crack, make sure the doors are sealed properly etc as HF and MF will leak through more easily than LF.
You seem to be contradicting yourself here: On the one hand you are saying that when sound goes through a small opening into a large volume of air, there are huge losses due to impedance mismatch, but then you are saying that when sound goes through the small gap under a door, there are NOT any large losses due to impedance mismatch, and the sound will still propagate into the room. This is confusing: Which side of the argument are you taking?
You are correct that small gaps can transmit a lot of sound. Here's a graph that illustrates that effect:
Unfortunately the quality isn't very clear, but I can't find the original right now to re-scan it. The X axis is the theoretical TL through a wall with no gaps, and the Y axis shows the actual TL. The curves show the degradation for various "open area" percentages. The top curve is for 0.01% open area, which works out to a hole the size of a pencil tip in a wall 8 feet high and 10 feet long. So, with a tiny hole that size, the isolation of a wall designed for 50 dB TL would actually be only 40 dB. That's a major loss in isolation. If the gap were 0.03%, the wall would only isolate at about 32 dB. Which is similar to what an ordinary house wall would get. a 0.03% open area gap would be something like a 1/16" gap under a door.... So you are right about small gaps allowing through a lot of sound, but that does seem to contradict your claim that sound going through small gaps into large rooms is greatly attenuated...
And also, if you have many holes or many gaps, especially in close proximity, then LF "sees" the sum of them.
Actually, that isn't true either. You should probably look into perforated panel theory to get a better idea of how that really works. It's a lot more complex than I can go into here in a few paragraphs, but the way that a perf panel attenuates sound depends on many factors, including the sizes of the holes, the thickness of the panel, the shape of the holes, the pattern of the holes, the open area percentage of the holes vs. the panel size, and a few other things. Its not simple at all. The overall effect is something similar to a comb filter, usually. There's an interesting paper on that, by Jaouen and Bécot, titled "Acoustical characterization of perforated facings", where they propose a method for predicting the results, under some limited circumstances. There's an even better paper titled "FURTHER INVESTIGATIONS OF PARTITIONS HAVING BUILT-IN ACOUSTIC TREATMENT" from the BBC, from back in 1995 IIRC, that has both theory and experiment in it, with some rather interesting results. There's also the more recent paper by Kingan and Pearse, titled "SOUND ABSORPTION OF POROUS MATERIAL IN COMBINATION WITH PERFORATED FACINGS", but that's more about acoustic treatment than TL in walls. Still, there's some interesting stuff in there. They examined the effect of the hole size, hole pattern and open area ratio, and how they interact. Their conclusions also apply to perforated walls, to a certain extent.
But a couple of holes (fresh air in/out, for example) coupled to acoustic flex duct which has a suitable length will usually be all that is needed for attenuating sound in/out of a room.
Maybe you could provide some theory and equations to support your claims? For example: how long does the duct have to be to reduce the sound of drums by, say, 50 dB? And what role does diameter play? Does it make a difference if the flexduct is made with Mylar, foil, or something else? Does the type and thickness of the insulation have an effect? Does it matter if the flexduct is completely stretched out to the full length, vs. being only partially stretched? There's a lot of variables to consider here, so I'm hoping that your equations take all of those into account. I'd be very interested to know what combination of factors I would need in order to get 50 dB TL through a tracking room wall, which is a typical example. Maybe you could show how to calculate that?
But, you may be surprised, or even shocked to know that many professional studios do not use silencer boxes for their HVAC, and simply use well positioned and properly installed acoustic flex duct.
Could you provide a list of those studios, with photos of their actual duct installations, so we can see how they did it? And of course, actual test results, showing the real insertion loss they obtained in each case. That would be interesting, and very useful for us studio designers. It seems like we could greatly simplify HVAC systems, if only we had the data that you seem to have. I'm sure our clients would be pleased with the reduction in costs, too. Just poking a piece of flex duct through the wall is an awful lot cheaper than building silencer boxes! I'm intrigued...
- Stuart -