The problem
In music studios, small venues, critical listening rooms, practice rooms or any other space for the serious listening of music, the room can sometimes cause effects which make for a worse experience. These can be 'boomy' or 'ringing' bass, or areas of the room where the bass felt completely lacking in energy. While fancy signal processing, room treatments and absorbers can alleviate the problem somewhat, it's best to reduce these problems at source, by optimising your room dimensions before doing anything else.
In this article we will learn:
- What are room modes and standing waves?
- What is the Golden Ratio of room dimensions?
- How best to predict the effect of room modes
- What can we do about room modes?
Back to basics: What are sound waves?
In order to understand these issues, we need to have a firm understanding of what sound waves are.
Sound waves are a fluctuation in air pressure detected by the human ear.
As a loudspeaker plays music, it moves back and forth, creating a wave of high and low air pressure which travels away from the loudspeaker.
The distance between peaks in air pressure is called the wavelength. This can also be measured as the distance between troughs.
The frequency of a sound is how many of these peaks and troughs the loudspeaker plays per second.
Low frequency sound (like bass instruments) have a long wavelength, while higher frequency sounds (like whistling) have a shorter wavelength.
For example, the musical note A2 (frequency 110 Hz) has a wavelength of 3.1 metres, while A4 (frequency 440 Hz) has a wavelength of 0.78 metres.
Standing waves
As sound waves bounce off of walls, they pass back over themselves creating constructive and destructive interference (remember that from school?).
If we imagine a piano playing and holding the note A2 (110 Hz), the sound wave will travel towards a wall, and then bounce off of the wall, passing back over itself and creating interference.
When the room dimensions are proportional to the wavelength (or in fact, half a wavelength), then the reflected sound wave will be somewhat in sync with the original sound wave, and this is where we get extreme peaks and troughs in fixed locations. These waves are known as standing waves, and these cause room modes – a broader term referring to the relationship between the room and the standing waves.
The animation below illustrates this phenomenon in a pipe. The peaks and troughs stay in one location, and are the same amplitude (loudness) each time. If the sound waves were not proportional to the pipe (or room) dimensions, then the reflected sound wave would be out of sync with the original sound wave, and the interference would constantly be constantly varying in amplitude (loudness), such that we don't experience the peaks and troughs as severely. When the wavelength of a given frequency is proportional to the length of the pipe (as shown below), this creates fixed peaks and troughs in the pipe. In a room, we would hear this as areas where a certain frequency sounds louder or quieter, and this is generally considered undesirable in a serious musical setting.
The modal frequencies are related to the room dimensions.
This pipe example only shows two dimensions, because it is easy to visualise. It’s analogous to a standing wave between a pair of room surfaces (front to back, side to side or floor to ceiling). These are known as axial modes. However, in three-dimensional spaces (like real rooms), standing waves can occur between more than one pair of surfaces. Tangential modes occur between two pairs of surfaces, or oblique modes can involve all six surfaces.
The Golden Ratio
As we’ve seen above, room modes are dependent on the dimensions of the room.
Over the past century, many researchers have tried to quantify the ‘ideal’ room proportions to reduce modal effects, or find a "Golden Ratio". The research has produced many different Golen Ratios, but none of them foolproof.
Each and every room will experience a modes to some degree.
In 1946, R. H. Bolt [1] defined a range of room dimensions which should provide optimum room response at low frequencies (that is, these room dimensions are thought to have the ‘flattest’ peaks and troughs). When plotted, these ratios fall within an area called the ‘Bolt Area’, and this is a commonly used heuristic to find optimum room dimensions. This is shown below, with ratios proposed by other researchers overlayed.
Bolt’s method is not without its shortcomings, however, and more robust methods have been proposed recently, but these require more complex computation instead of a simple rule of thumb. See [2].
Computer modelling and computation
While heuristics and rules of thumb offer a good starting point for investigating room dimensions in a new studio or music room, the most accurate answer will come from 3D modelling used specialised software. In this way, the acoustic designer can produce heatmaps which show us the modal peaks and troughs at a given frequency, and make recommendations to reduce these effects. At Timbral, we have experience in room acoustic modelling for music studios and venues, and specification of mitigation to reduce the effect of room modes on your listening environment. Get in touch with us for no obligation chat to see if we can help with your project.
Which rooms are affected by room modes?
Strictly speaking, all rooms have modes, but they only become a problem when there are too few modes around a given frequency.
With high frequency sound, there are lots of modes at many different frequencies and directions. In acoustics jargon, we would say these modes are diffuse. When this happens, the standing waves combine to produce a fairly ‘flat’ response, without large peaks and troughs.
With low frequency sound, the modes are few and far between. This means that we experience the peaks and troughs without much interference from other standing waves at similar frequencies, so we get the full peaks and nulls when listening to bass sounds. This is what creates areas of “boomy” or “dead” bass in different parts of a room.
The cut-off frequency where modes stop being problematic can be estimated using the Schroder equation. This cut-off frequency decreases as the room volume increases. Meaning that, in large rooms, low-frequency modes are diffuse, and therefore not problematic. Generally speaking, in rooms above 1,000 m3, low frequency modes are unlikely to be problematic.
Modes are generally a problem associated with smaller rooms, and at frequencies up to 300 Hz.
What can we do about room modes? And what if you can't change your room dimensions?
It's all well and good discussing room dimensions for music rooms being newly built or undergoing a significant refurbishment, but what about existing music rooms experiencing these problems?
The good news is that we can reduce the effect of room modes by providing absorption at the affected frequencies. Given modes are generally only problematic at low frequencies, the most-commonly used absorbers are bass-traps. These are specialised absorbers which are most effective at low frequencies.
Absorption has the effect of damping the modal response. That means it reduces the peaks and troughs of the standing waves, thus providing a flatter (and more desirable) room acoustic.
Providing targeted absorption at low frequencies will reduce the effect of room modes.
Summary
- 'Boomy', 'dead' or 'ringing' bass notes are caused by room modes.
- Standing waves and room modes occur at frequencies whose wavelengths are proportional to the room dimensions.
- All rooms experience modes, and there is no single Golden Ratio.
- Room modes are generally only problematic in small rooms, and at low frequencies up to 300 Hz.
- To reduce the effect of modes, we can introduce low-frequency absorbers (bass traps) into the space.
References
[2] Professor Trevor Cox, Room sizing for studios, University of Salford.
See also: How reverb and rooms affect our percception of music, The Ultimate Guide to Setting Up Your Audio Suite.
