I found the following (apparently approximate) formula to calculate transmission loss in a single leaf wall: TL = 20 * log10 (ms * f) - 48, where ms is the mass per unit area and f is the frequency. Graph is attached to this post but I calculated 47dB attenuation at 63Hz.
That's called the "mass law" equation, and is used for calculating the average isolation of the one-third octave band centered on the frequency given by "f". It is not used to calculated the isolation at a specific frequency. So you won't be getting "47 dB at 63 Hz." but rather "approximately 47 dB across the entire one-third octave band centered on 63 Hz, which extends from 44.7 Hz to 89.1 Hz".
There's a simplified version of the Mass Law equation that estimates the isolation across the entire spectrum:
TL = 14.5 log (Ms * 0.205) + 23 dB
Where: M = Surface Mass in kg/m2
According to that, you would be getting about 55 dB from that 35cm concrete slab.... assuming that that there are no windows, doors, holes, cracks, skylights, or walls that have lower isolation.
Right wall: 11cm thick, hollow concrete blocks, supposedly 10cm with mortar finish. The section right above the door is 7cm thick, made of hollow bricks with the same mortar finish. The glass areas are 4mm thick, mounted on metal frame with joints that look like plaster but I think it's not exactly that. The door is full wood and glass. Glass is probably 4mm, wood 45mm excluding a section underneath the glass that's more like 20mm.
The weak spot there is obviously the glass, then the door itself, then the section above the door. The isolation of the room is only as good as the isolation at the weakest point, so basically all that concrete in the ceiling above doesn't really matter, until you take care of improving the isolation of the door, glass, and header. Mass law says that 4mm glass will give you about 37 dB, but for the 63 Hz band it would only be about 8 dB. So that's how much total isolation you'd be getting for your room: about 8 dB for the 63Hz band.
So when it comes to isolation, I reckon that the biggest issues (aside, obviously from the various openings inside the room) are the right wall, and the ceiling, since the latter is the only thing standing between the studio and the neighbors (aside from a little distance and their double glazed PVC windows.)
Not really: Once again, the total isolation of the room is only as good as the weakest isolation. Once the sound gets out through the weakest part, it is free to expand outwards from that point, especially low frequency sounds, which are not very directional.
So your plan should be to work on those areas that are the weakest, and bring them up to the same isolation level as the rest of the room.
I'm not too sure what to make of the backwall. Airborne sound through the wall shouldn't really be a problem
Why? Sound that gets through that wall has left your studio, and is now in the "outside world". ...
Since the floor is on solid ground and the wall really massive I'm guessing that vibrations from the floor won't really transmit upwards.
It's never a good idea to guess with acoustics! Structure-borne impact noise will be audible throughout the entire structure. If you expect to be transmitting vibration or impact noise into the slab, then you should design something to prevent that: a simple drum riser would work.
Or could airborne sound in the studio hitting that wall transmit itself through the structure right up to the first floor and above?
Yes. That wall is a flanking path from your studio to the outside world.
I have to admit that I really don't know how much I should worry about structure-borne noise in my situation.
It can be a major problem, going in both directions. If you plan to play drums in your room, then you have a potential impact noise issue. Ditto if you plan to have a loud bass cab sitting on the floor, or anything else that directly touches the slab. Likewise, if you have noise sources outside the room but in contact with the building structure, such as pumps, fans, doors slamming, people walking on floors, water in pipes, washing machine, dryer, etc, then you have a potential problem.
Basically I would love to have 9m2 of free space inside the room. I pretty sure I can keep front wall treatment and console desk to 3.5m2. So that would leave around 2m2 for isolation and the rest of the treatment which I fully realize is far from ideal and probably not enough.
It would ba a mistake to plan your acoustic treatment in terms of square meters of floor area. Rather, design the actually devices that you will need to attain ITU BS.1116-3 or EBU Tech.3276 specifications. Start with the simple, bulky options, and see how that works out. If you see that those will use up too much space, then you'll need to substitute for the more expensive, more complicated types that take up less space.
That said, a small room like that is going to need a LOT of treatment, especially for bass trapping.
You don't have many options for the location of your desk: your room is only 4.3 m long, so the mix position will have to be n the room center-line and about 160 cm from the front wall. That's it. Your speakers will have to go up tight against the front wall, with a 10cm gap for inserting a panel of OC-703. The speakers will be set up about 95cm from the side walls (putting them 150 cm apart, at a height of about 124 cm, roughly. They will be aimed at a spot about 40 cm behind the mix position, so roughly 200cm from the front wall, on the room center-line.
I really want to avoid doubling up all the walls with 300mm wool
You would not need that much insulation. Typically, it would be about 100mm, and since that fits in the stud bays, you don't lose more than that plus the thickness of the sheathing, for the total wall thickness. Maybe 130mm or so, total.
really want to avoid ... adding 1m of bass trapping on the back wall.
Most of the rooms I design have about 50cm or so of bass trapping across most of the rear wall, with a bit more in the corners.
. I do realize that I will probably need quite a lot of treatment for bass due to the thick walls.
Not due to the thick walls, no. They are irrelevant here. The reason you need a lot of treatment is due to the size of the room. That's the main factor here: it is a very, very small room, so it will need a LOT of treatment. It's the SIZE of the room that mostly determines how much treatment it needs.
I'll certainly have to find the right balance between the space I want to keep and the amount of treatment I want to put up.
Most people do things the other way around: they first determine what treatment will be NEEDED to get the room to produce the acoustic response they want, then try out different treatment options to see which ones are the best match for them, in terms of the space they take up, and their budget. Cheap treatment takes up lots of space. More complex treatment that takes up less space is more expensive. But there are limits: Even the most expensive, lowest profile bass traps still take up considerable space, especially in small rooms.
I really want to keep the opening in the ceiling that lets the daylight in ... as well as keeping a glass bay between the corridor and the studio
So you really don't want good isolation for your studio?
So anyways, what I will be definitely be doing in terms of construction work is doubling up the right wall since that is most likely the weakest spot in terms of sound spillage
That would be a waste of money. Seriously. As I said several times above, the isolation of your room is only as good as the weakest part. You already have the mass law equations, so now you need to sit down with pencil and paper, to calculate the isolation for each part of each wall, ceiling, window, door, etc. Find the lowest number: that's where you need to start, to improve your isolation. Work on the WEAKEST elements, as shown by the math, not by guessing. Once you have all the weak parts taken care of, then you can do the math all over again, and see if the new lowest number is higher than the amount of isolation that you need. If not, then keep on going!
Just building a wall on one side will NOT solve your isolation problems. If you don't isolate ALL sides of the room (including ceiling, walls, doors, windows, HVAC, electrical system, and possibly also the floor, under some conditions), then you won't have any isolation at all!
Think of this: Imagine there's a guy who wants to have an aquarium in his living room, because he likes to look at fish, so he goes to the store and buys a metal frame to make his aquarium. But then he thinks: "I only need to see them from the front, so I'll just buy one sheet of glass to put on that side, and leave the rest open". How well do you think that aquarium will hold water?
Obviously, it won't hold water at all! But that is what you would be doing if you only isolate one wall...
In other words, if you do need to isolate your room from anything, then you need to isolate it from everything. You cannot isolate a room in only one direction, just like you cannot build an aquarium with glass on only one side. As soon as you put water in it, the water will simply gush out and splash all over, in ALL directions, even the direction where the glass is, since the water will go over, under, and around that glass. If you only isolate one side of your studio, then when you "pour" sound into it, the sound will gush out and splash all over, in all directions, including the direction where that one isolation wall was, because the sound will go under, over, and around that wall, as if it wasn't even there.
Therefore, if you do need isolation, then you need to build the same amount of isolation in all directions around your room, and in all aspects: every wall, ceiling, door, window, electrical conduit, HVAC duct, and everything else, must all be isolated to the same level. Acoustic isolation is only as good as the weakest point, so if you isolate your studio fantastically all around except for the window, then you might as well not isolate anything, because sound will take the "easy" path out through that window...
I will in all likelihood double up the ceiling too,
See above: same reasoning. A waste of money if done on its own, without also doing the walls, windows, doors, HVAC and electrical.
I'll have to keep that pretty thin (and will probably implement something along the lines of John Sayers' "inside out" ceiling arrangement).
When we build inside-out ceilings as part of the isolation system for a studio, that inside-out ceiling MUST rest on the new inner-leaf walls (which might also be inside out, to save space....). An inside-out ceiling that is attached to the outer-leaf walls, does not provide much isolation at all, due to flanking....
I'm having trouble figuring out if I can achieve enough isolation for drums.
Drums played normally produce around 110 dBC to 115 dBC, and played hard can be twice as loud. Let's assume that you will only every play them normally, at 115 dBC. Your weakest weak point at present is the thin glass, apparently, which will get you around 30 dB of isolation (realistically, in real life): So your drums inside at 115 dBC will be producing about 85 dBC outside. To make that inaudible, you would need to get it down to about 35 dBC, so you would need another 50 dB of isolation, in addition to what you get from the glass.
If you decide that you will only mix in there, never track, then the "rule of thumb" is that most engineers mix at around 80-85 dBC, and occasionally turn it up to around 100 or 110 to "check the bass". So at normal levels of 85, your glass would be getting that down to about 55 dBC outside, and you'd need another 20 dB isolation to get that inaudible.
the goal is not to have complete silence right on the other side of the studio walls but to avoid bothering the neighbors living in the building which are two floors up
So one of your priorities MUST be to prevent sound from getting into the building structure.
two floors up - are more exactly, 35cm of concrete, 3 meters of air (for the closest ones) and a double-glazed window away
No. You said that you have a skylight in the ceiling that you want to keep, so that is the only thing separating you from the neighbors. Double-glazing is not much use for isolation low frequencies, such as drums, bass, keyboards, and electric guitar.
I'm supposing that there's only three significant ways the sound could travel up to the neighbors.
... And also the "I really want to keep the opening in the ceiling that lets the daylight in ... "...
So, from here, I suppose I need to make the following measurements.
What you need to do, is to get a decent quality sound level meter, then set up a full-range speaker in the room, and play bass-heavy contemporary music through it at 115 dBC, measured in the room about a meter away from the speaker. Now take your meter and go measure at many, many locations outside the studio, both inside the building and outside the building, including inside your neighbor's homes. Then turn off the sound system, and measure the ambient noise levels at the exact same locations. With that information, you can calculate how much isolation you have at present, and how much extra you need.
Don't guess! Do the actual measurements, with your meter set to "C" and "Slow", and make notes. Then do the math.
For the ceiling, I don't think I could currently make any meaningful measurements.
I don't understand why not! In what way would the procedure that I just outlined, fail to take into account the ceiling? You cannot judge your total isolation by thinking about individual parts of the room: the room is a SYSTEM, not a bunch of separate paths. The entire room (including the ceiling) currently produces a certain level of isolation, which will be measured by the procedure above. That's what matters: the TOTAL isolation you are getting at present, as compared to how much isolation you NEED to get. Trying to measure the isolation of each part of the room by itself is pointless at this stage: All that matters is the TOTAL isolation. Once you have measured that, then you can try to figure out where your weak points are, and beef them up, then repeat the same procedure , to see if you have enough isolation yet.
I need to figure out how much isolation could I achieve with something 25mm gypsum board and a thin gap, maybe 4cm, filled with fiber wool insulation... I tried to looking for data concerning similar structural arrangements to this but didn't manage to find anything meaningful.
You could not find anything meaningful to answer that question, because you are not asking the right question!
25mm of gypsum board with a thin gap of 4cm filled with insulation, up against a concrete wall, will give you an MSM resonant frequency of around 55 Hz, and therefore it would not isolate at all below 78 Hz. It would only isolate somewhat starting at around 112 Hz, and would isolate well starting at about 162 Hz. Total isolation at resonance would be around 10 dB, rising to 42 dB at 250 Hz, for a overall total isolation of around 60 dB.
I also tried looking for data concerning double glazed windows (something along the likes of 4mm glass / 6mm air / 4mm glass) which is the standard thing you'd find here.
Based on standard MSM equations, that would give you an resonance frequency of around 340 Hz, very poor isolation below about 480, and decent isolation above about 690Hz. Total isolation around 36 dB, but really lousy in the low end (only 24 dB at 500 Hz) so STC-20 would be about right. Double-glazed units are not good for low frequencies: only useful for mids and highs. There's also the major issue of coincidence dip to consider, around 4k for typical glass.
1 - Should I worry about flanking issues and structure borne transmissions from the walls?
Yes.
2 - Does anyone have better isolation data for double glazed windows than STC curves?
See above. Also, these might be useful:
glass-isolation-for-typical-double-glazing.jpg
glass-isolation-for-typical-double-and-triple-glazing.jpg
As you can clearly see, isolation from double-glazed units is very lousy in the lows and low-mids No use at all for studios. You only get reasonable isolation above about 1 KHz, but then coincidence kills that again at around 4 kHz.
3 - How much increase in isolation could I gain by doubling up the 35cm concrete ceiling with something like 25mm gypsum boards and a few centimeters of fiber glass wool?
As above: about 60 dB, which is getting close to your flanking limit.
To make up for the fact that it doesn't give as much isolation in the low frequencies as I was hoping, I compared it with our hearing threshold per frequency
I don't understand why you used the threshold of hearing. That makes no sense. You should have used the curve that describes the EXPECTED level at the receiver, probably the 50 phon curve in your case, or maybe the 60 phon. You seem to be misunderstanding what those graphs are showing you...
- Stuart -
) and I'm taking the opportunity to upgrade to a more professional setup. Maybe this should go into the Studio design forum since the room is already existing and I'm not planning on making a lot of construction work but my first questions (which are quite specific to the room btw) seem to belong here...
but right now it's dinner time