From the March/April 1977 issue of the late, great Recording Engineer/Producer (RE/P) magazine, the principals of Abadon/Sun Studio, which was located in San Antonio, TX, look at the practical and technical sides of studio design.
We at Abadon/Sun decided to write this article because we felt a large number of small studio owners required more information to properly design and build their first studio.
What we’ve tried to do is to simplify things as much as possible and provide the builder with the design fundamentals.
Since most small control rooms are rectangular in shape we’ll detail the design considerations for a room of that shape. Our primary goal is to eliminate severe resonant modes in the room and establish the low-frequency response of the room through the proper selection of room dimensions.
A room with parallel surfaces and no acoustic treatment will exhibit resonant modes between opposite surfaces. That is, we will have resonances created between the two side walls, the front and rear walls and the floor and ceiling surfaces.
When selecting the various room dimensions the objective is to avoid common resonances between any of the room modes to avoid build-up of sound at the resonant frequencies (Figure 1). If a common resonance is present, it will probably result in an increase in volume of that one frequency producing a very boomy sound (for low-frequency resonances). Since the low frequencies are the main source of difficulty in room design (and are the hardest to correct) this article will concentrate on them.
The frequencies at which resonance occurs are determined by the distance between the two walls under consideration. The formula for the resonant frequencies is:
where d is the room dimension (in feet) and fn is the resonant frequency (in Hz. or cycles/second). The resonances will occur at multiples of the fundamental frequency f(I). For that reason we use the multiplier (n). For example, two walls separated by 10 feet will produce resonances at 56.5 Hz., 113.0 Hz., 169.5 Hz., etc. By this method the resonances occurring in the room can be readily calculated. Considering a room 10′ x 15′ x 20′:
Our conclusion from these calculations is that 10′ x 15′ x 20′ is a very bad choice of room dimensions. The reason is that we have a resonant frequency (113 Hz.) common to all three room dimensions. This would produce a very bad room resonance every time we encountered a 113 Hz. signal which would probably occur fairly frequently.
Changing our choice of dimensions to 10′ x 14′ x 22′ and applying the same equations we find these resonant frequencies:
As can be seen, there is no common resonant point between the dimensions selected this time. One limitation we will impose on your choice of room dimensions is that the ratio of dimensions should lie within the limits of the graph given in Figure 2. For example, a room measuring 10′ x 11′ x 18′ would have a ratio of dimensions of 1: 1.1: 1.8 which would not be acceptable. A room with dimension ratio of 1:1.4:2.2 is within the acceptable range.
[NOTE: Some of the ratios within the limits of the graph may produce undesirable additive resonances. For this reason, you must check them thoroughly by calculating the resonant frequencies before committing yourself to a selection.]
Another calculation which will enter into your choice for dimensions is the diagonal dimension of the room. For a room to reproduce low-frequencies well, there has to be a sufficiently long dimension to allow the low-frequency waves to propagate themselves. The equations are:
The room diagonal can be found from the equation:
From these equations, you should be able to determine the lowest frequency that can be propagated in the room. The diagonal lengths required for some sample frequencies to propagate are given as:
Looking at another example, a room 9′ x 11′ x 14′ is suggested. The ratio of dimensions is 1: 1.2: 1.6 which is acceptable according to our graph of acceptable ratios. The lowest frequency will be:
Room resonant frequencies are:
From these calculations, we can see that this is an acceptable choice of dimensions.