Bass á la mode
Perfecting the acoustics of your studio
If studio design has a golden rule, it's don't be square (daddy-o). Stuart Litobarski concludes his analysis of studio acoustics with a look at the virtues of a rectangular outer shell and the nature of room modes...
In our previous article on the reflection-free inner room of the studio, we explored the use of shape as an acoustic tool. This month we look at the massive outer shell and its all-important low-frequency modes.
You will see that when designing the outer shell, it isn't necessary to depart very much from the basic rectangular shape. Having a rectangular shape of shell makes it far easier to get your room modes absolutely spot on, by adjusting the ratio of the room length and width to the height dimension. We will go on to see how, in a live room, a slight splaying of walls will effectively eliminate flutter echo, but no amount of splaying can correct those all-important low frequency modes. It is necessary to get the room ratios correct.
Modes occur only in rooms - outdoors you can have no room modes, only something known as evanescent wave propagation. Inside the studio we're especially interested in bass modes, for reasons that we have mentioned in the previous articles. Modes can be defined as the frequencies which are the solutions to the wave equation when bounded by the three dimensions of the room. What that boils down to is that the room acts like an organ pipe, with the walls forming the end stops. If the walls are relatively wide apart, the frequency of the mode is low. If the walls are closer, the frequency will be higher.
It probably won't surprise you to learn that there are three different types of mode. Axial modes occur between a pair of opposing walls. There are two other types of mode in a rectangular or normal shaped room - they are called the tangential and oblique modes respectively. These last two modes are where sound hits more than just two opposing walls. They are usually at a much lower level than the axial modes, so for most purposes may be considered negligible, and ignored. Each pair of walls, and the floor and ceiling, generates its own series of modes. Starting with the fundamental, there are then overtones or harmonics at twice the fundamental frequency, or three times and so on, just as with a musical instrument.
The modes for each of the side walls, the end walls, and the floor and ceiling have their own harmonic series. The overall result for the room modes is the addition of all these. As you can see from the mode plot showing a defective room, there are gaps between some of the modes, while other frequencies coincide. This happens when the room has length, width and height, which are simple multiples of each other. For example, the length may be exactly twice the width. This means that the harmonic series for each pair of walls will fall on top of each other, or coincide, at particular frequencies only, giving rise to the phenomenon of standing-waves.
So how do we tell a good mode when one slaps us in the face? Well, modes and their harmonics should ideally be spaced at intervals of no more than 20 Hz apart, so that there are no big gaps, which would create unresponsive lulls. Nor should there be any modes occurring at the same frequency, which reinforces certain frequencies at the expense of others. This makes square rooms a bad idea.
It's all to do with the relationship between modes and nodes, or more particularly the nodes and anti-nodes of the standing-waves within the room. You might say they are the same thing looked at in a different way. If the modes are poor then the room will suffer from poor diffusion. So you could find it difficult to get a good sounding spot within the room when positioning a microphone. However, I hear you say, you actually like the strident yonks and rings that a peaky room response gives. Well, why not add that effect electronically, at the mixing stage, in a far more creatively controllable way.
The overall shape of the room affects the way that music played in it will sound. For proof of this you need look no further than your own bathroom. Try singing chromatic scales in the bath, and you will soon hit upon a few room resonances. In most bathrooms this test works best with the male voice, so borrow one for the demonstration if needs be. The aim is to find room dimensions whose ratio generates modes that are evenly spaced.
There are certain golden ratios that have stood the test of time. The Greek philosopher Pythagoras was particularly crazy about golden ratios. The western diatonic scale is actually built this way. Let's look at a few of these golden or preferred ratios now. Many text books on studio acoustics will give ratios such as 1 : 1.14 : 1.42. What do they actually mean? What these ratios mean is that the distance between each pair of opposing room surfaces, such as floor to ceiling, or side-wall to side-wall, should form a simple ratio.
How is a musically literate person, who may not actually be a mathematical genius, going to put that into practice? Well, the smallest distance is usually the floor to ceiling height. So this is taken to be unity, or one. The other wall distances are arrived at by multiplying the floor to ceiling height in the given ratio. So, for example, if you have a standard ceiling height of 2.46 metres, then your side walls should be spaced by 2.80 metres, and your end walls should be 3.47 metres apart, to fit the above ratio.
Of course, there are many other satisfactory ratios, and in practice you often have to make the best of what you have. However, if your plans involve building walls in your studio, then this knowledge could be valuable to you. So if you find yourself building from scratch, go for one of these preferred ratios, or have your proposed room dimensions checked out by a qualified acoustician.
The most interesting area for modes is from the lowest audio frequency, nominally 20 Hz, up to around 300 Hz or so, which is called the Schroeder frequency. The Schroeder frequency is related to the bandwidth of each mode, and, for those who can work a slide rule, it's defined as:
fSchroeder = 2000 SQRT ( RT / v )
where RT is the room reverberation time, and v is the room volume (metric).
Above this Schroeder frequency the modes will inevitably be quite smooth, regular and evenly spaced, and no special considerations need be taken. The frequencies of interest cover all the vocal range, and can be really quite audible to the trained ear, especially in a live room. We must ensure that the room ratio has the correct proportions to generate a good distribution of modes, at all frequencies below the Schroeder frequency.
Room-within-a-room studios often make use of a lightweight inner room, in combination with a massive outer shell, to provide good soundproofing. Low-frequency sound waves don't necessarily stop at the lightweight inner carcassing. High energy bass frequencies will chiefly see the outer, more massive walls, rather than the flimsy inner walls.
Technically, the acoustic impedance of the composite surface becomes increasingly complex at very low frequencies. More especially since the wavelengths of bass-frequency sound are likely to be long, relative to the dimensions of the inner room. It remains important that the outer shell should be dimensioned with the modal distribution very much in mind. The low frequency modes are the most important to us here.
The low frequency modes are adjusted by varying the ratios of the outer massive shell, to make the predicted distribution of modes as smooth as possible. Do we need to splay the walls of the outer massive shell? As we saw previously, to have any effect at all on sound, the variation in room geometry needs to be large in comparison to the wavelength. The small variation in shape that comes from splaying the walls is negligible in comparison to the long wave-lengths at low frequencies.
There is probably little benefit therefore in making the outer shell deviate much from a basic rectangular shape. Indeed, a very odd shaped live room may have a modal distribution that is difficult to predict using current software. However, splaying the walls of the outer massive shell can serve to distribute any standing-waves within the cavity that separate the inner-room from the outer-shell. If the surfaces of the inner room contain bass trapping, then that is another valid reason for splaying the massive shell, to allow for different depths of bass-absorber.
Live rooms are somewhat different, because they often have no inner-room, so the walls define both the high and the low frequency performance. The ratios need to be correct, for good low frequency modes, and the walls also need to be adequately splayed, to eliminate flutter echo.
In a live room you will often find two adjacent walls splayed inwards, with the corner diametrically opposite being left square, for the reason we looked at earlier, that you only need to treat one in each pair of opposing walls to completely cure flutter echo. The wall plan of Mr.Grin studios shows clearly how this principle can be put into practice.
The Schroeder frequency increases with reverberation time. Increasing the reverberation time, from 0.2 second to 1 second, effectively doubles the low-frequency range where care is needed with the modes. You can see why extremely live rooms, such as stone rooms, will be quite temperamental regarding their modes. They will require careful design if they are to be completely free from standing-wave type defects. Conversely, in very large, or in acoustically dry rooms, the Schroeder equation tells us that the exact location of the modes is less important. Adding absorptive materials, such as acoustic tiles, does tend to smooth out those troublesome modes. That's because well damped modes have broader bandwidths.
In a room possessing good modes, you should find it far easier to locate a satisfactory hot-spot with your microphone. You should also find that your far-field mics pick up a better sounding room ambience. Remember, many top singers will actually pull-off from the microphone at the end of a phrase, allowing the compressors to bring in a little of the room quality. So there may be something in it after all.
Stuart Litobarski is an Electronic and Acoustic Engineer, as well finding time to play bass with Bristol acid-jazz band 'High Jinks'. His company, Soundwave Acoustics, specialises in studio design and acoustics consultancy.
Feature by Stuart Litobarski
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