RT60 limits

[Andrew Steel]

Hi All,
Can anyone please point me at a source of the way to calculate the recommended upper and lower limits for RT60 based on room size?

Thanks
Andrew

[Scott R. Foster]

Andrew:

I don't believe there is such a calculation... its more of a range of norms.

As I understand the issue, it aint just a matter of room size, your application also comes into it... a tracking room of 8,000 cubic feet used to record acoustic instruments might have an average reverb time across the band of .75 seconds... a similarly sized room used for a death metal band's rehearsal space might need to be half that to work out.

Everest's "Master Handbook of Acoustics" has a discussion of this and a little chart... but you are warned in the text to take the chart with a grain of salt.

If you describe your room size and application I'm sure you'll get some suggestions.

[avare]

For studio spaces it is wide open as Scott wrote.

If you are referring to control rooms, the evolving standard is 0.25*((refv/roomv)^.3333), where refv is reference room volume (100m^3) and roomv is the room volume. Standards for tolerances across frequency ranges etc are described in, amongst others, AES TD1001. I don't have the url but it is on the web with more information and additional references.

[Bob]

How do you define reference room volume, vs room volume ?

[avare]

How do you define reference room volume, vs room volume ?

I was trying to write quickly and use the terminlagy in the specifications. A bit more mathematically expressed:

refv=100m^3
roomv=volume of the room being designed

Hope that makes it clearer.

[Bob]

So the formula is

Incorrect Formula:
Control Room Recommended RT60 = 0.25 * (( 100 m^3 / ProposedRoomVolume ) ^ .3333)

New Formula (based on Avare's comment below):
Control Room Recommended RT60 = 0.25 * (( ProposedRoomVolume / 100 m^3 ) ^ .3333)

[avare]

So the formula is

Control Room Recommended RT60 = 0.25 * (( 100 m^3 / ProposedRoomVolume ) ^ .3333)

Correct!

[Savant]

Folks,

First, the document being referred to here can be downloaded from AES at:
http://www.aes.org/technical/documents/AESTD1001.pdf

Second, it might be worth noting that the RT60 recommendations from this document also state tolerances of ±0.05s between 200 and 4000 Hz. These are tolerances for average RT60. In other words, you should - in practice - evaluate the RT60 at no fewer than 4 positions in the room (more if you can) and average the results to determine whether the criteria have been met. One thing spreadsheets won't typically show you is the position dependence of RT60. This makes sense since your predictions are statistical - inherently averaging all locations in the room.

In design, many of you are already aware of my reluctance to use RT60 as a primary predictor for any small room. "Small" being < about 10,000 ft³ (or < about 300 m³). If you approach the room as a discrete reflection challenge, you will typically reduce the RT60 to meet the criteria being discussed here by default.

[Andrew Steel]

Thanks all for the replies.

I guess I can make my requirement a bit clearer :-) I am putting a softeware tool together for my own use and to embed the theory a little deeper in my head - may sound weird but it works if I work with something at a level where I am forced to understand first principles rather than just apply the formulae.

My question is what the source is for generating the typical limit lines seen on graphs of reeverb time like those in CARA. The upper limit generally seems to rise at low frequency and the lower limit seems to slope down at high frequency. I know there must be variations based on room volume, application etc and that they are empirically derived. I expected tables or formulae with 'ranges' like those for room ratios in a book or two.

Jeff,
I am also very interested in the position dependance of reverb if you have any good references?

Thanks again everyone.
Andrew

[Bob]

Avare:

I entered that formula into excel and created this

ft^3 m^3 RT60
1000 28.3 0.38
10000 283.2 0.18

This is just FYI. I am of course paying attention to Jeff !

edit: This is bad data with the incorrect formula, so I've removed most of it. See the post below.

[Dan Nelson]

Am I missing something? the rt60 is decreasing as the room gets larger ?

Dan

[Savant]

Andrew,

My question is what the source is for generating the typical limit lines seen on graphs of reeverb time like those in CARA. The upper limit generally seems to rise at low frequency and the lower limit seems to slope down at high frequency. I know there must be variations based on room volume, application etc and that they are empirically derived. I expected tables or formulae with 'ranges' like those for room ratios in a book or two.

For sources on the ranges, if I'm not mistaken, they have simply been derived over the years through subjective studies. Comparisons of the studies versus what is measured versus what is predicted give us the upper and lower limits we use today. Anyone else know more/different?

For ranges of RT60 that are generally acceptable for different types of rooms, you can look in almost any acoustics text. Beranek and Harris come to mind immediately.

Jeff,
I am also very interested in the position dependance of reverb if you have any good references?

Well, it just is. I mean, RT60s are statistical values. By measuring them, we have removed some of the statistical nature of the quantity.

Analogy: Knowing racecars going around a track average 210 mph doesn't tell you who won the race. And vice versa: Knowing the top speed was 215 mph doesn't tell you the average speed of, say, 33 cars. (Got Indy 500 on the brain, folks! It's May: You can't get away from it in this town!)

RT60s do not take into account any of the idiosyncracies of different positions in the room. The predicted values are taking the general characteristics of the room - volume and surface areas of different materials - and giving you a single value (for the frequency of interest - which by itself is a "big picture" since you're usually looking at octave bands and not discrete frequencies). An average, if you will. There is nowhere in a room you'll be able to measure that value since the formula used to predict RT60s eliminates the position dependence via statistics. To get an idea of whether your predictions are close to what's actually happening, you need to take multiple measurements.

Example: Measure the RT60s behind a couch and see what you get versus placing a mic in the middle of the room, away from any furniture. The position relative to a large absorber like a couch will skew your data. In the prediction, you have simply included "couch" as a line item with some number of Sabins added to the room. This reduces the average. However, if the couch is clear across the room relative to where you are, the RT60s might not seem/measure all that low.

For a complete treatment on RT60 and how we've gotten to where we are, you might look up the Collected Papers on Acoustics by Wallace Clement Sabine. Copies are available through the ASA.

[avare]

Bob:

As Dan wrote, something is wrong. What it is is that I wrote the equation wrong. The reference volume should the denominator, and the design room volume should be the numerator.

Now I know how the Helmholtz absorber error got spread so much.

[Bob]

Avare (and Dan):

Control Room Recommended RT60 = 0.25 * (( ProposedRoomVolume / 100 m^3 ) ^ .3333)
1 cubic foot = 0.0283168 cubic meter

Gives a typical excel spreadsheet line
A3 = A2+250
B3 = A3 * 0.0283168
C3 = 0.25 * (( B3 / 100 ) ^ 0.3333)

ft^3 m^3 RT60
63 1.8 0.07 (shower stall - waterproof acoustical treatment required?)
1000 28.3 0.16
1250 35.4 0.18
1500 42.5 0.19
1750 49.6 0.20 (approximately 16' x 16' x 7')
2000 56.6 0.21
2250 63.7 0.22
2500 70.8 0.22
2750 77.9 0.23
3000 85.0 0.24
3250 92.0 0.24
3500 99.1 0.25
3750 106.2 0.26
4000 113.3 0.26
4250 120.3 0.27
4500 127.4 0.27
4750 134.5 0.28
5000 141.6 0.28
5250 148.7 0.29
5500 155.7 0.29
5750 162.8 0.29
6000 169.9 0.30
6250 177.0 0.30
6500 184.1 0.31
6750 191.1 0.31
7000 198.2 0.31
7250 205.3 0.32
7500 212.4 0.32
7750 219.5 0.32
8000 226.5 0.33
8250 233.6 0.33
8500 240.7 0.34
8750 247.8 0.34
9000 254.9 0.34
9250 261.9 0.34
9500 269.0 0.35
9750 276.1 0.35
10000 283.2 0.35
11000 311.5 0.37
12000 339.8 0.38
13000 368.1 0.39
14000 396.4 0.40
15000 424.8 0.40
16000 453.1 0.41
17000 481.4 0.42
18000 509.7 0.43
19000 538.0 0.44
20000 566.3 0.45
22500 637.1 0.46
25000 707.9 0.48
27500 778.7 0.50
30000 849.5 0.51
32500 920.3 0.52
35000 991.1 0.54
37500 1061.9 0.55
40000 1132.7 0.56
50000 1415.8 0.60
60000 1699.0 0.64
70000 1982.2 0.68
80000 2265.3 0.71
90000 2548.5 0.74
100000 2831.7 0.76
125000 3539.6 0.82
150000 4247.5 0.87
175000 4955.4 0.92
200000 5663.4 0.96
225000 6371.3 1.00 (approximately 100' x 100' x 22')

I don't have any rigid fiberglass absorbers in my shower, and I sound pretty good in there !

[avare]

Bob:

I forgot to write something in the last post. Thanks for double checking the equation.

[Andrew Steel]

Thanks everyone for your replies. Thanks Jeff for such a good explanation!

Andrew

[Bob]

I came across this quote today, which looks very similar

[The ITU RT60 specification for rooms < 12,000 cu. ft is specified in the form:
RT60 @ 500 Hz = 0.3 *{(volume cu ft / 3531.34 cu ft)raised to 1/3 power} ]

http://www.avsforum.com/avs-vb/showthre ... ost2440755

[Paul Woodlock]

I came across this quote today, which looks very similar

[The ITU RT60 specification for rooms < 12,000 cu. ft is specified in the form:
RT60 @ 500 Hz = 0.3 *{(volume cu ft / 3531.34 cu ft)raised to 1/3 power} ]

http://www.avsforum.com/avs-vb/showthre ... ost2440755

Come on BOB!!! Start building your listening room. We need another build diary :)


Paul

[Bob]

Here's a link about the same topic
http://www.avsforum.com/avs-vb/showthre ... did=332289

Paul

Come on BOB!!! Start building your listening room. We need another build diary :)

The idea has crossed my mind. At the moment I'm stuck with another catch 22 about building code required room height vs ceiling construction.

[Acousticstudent101]

I have been searching for three hours to try and find the answer to a question and I know someone here must know the answer. OKAY here it is...

In Sabine's RT60 formula where did he get the constant? .049 Why is that the constant and what does .049 feet mean?

Someone please help me figure this out