Eigentones, standing waves, resonant eigenfrequencies, room modes. They go by many names but they all come down to the same concept: frequencies that reinforce themselves within an enclosed environment because their wavelength is an exact multiple of one—or more—of the enclosure’s dimensions.
..but what are room modes really?
For example, let’s imagine a band’s rehearsal space. The band is playing a song, and every time the bass player plays one specific note, the entire room seems to buzz. This buzzing is a specific frequency reinforcing itself because the physical length of this wave exactly fits between the distance between two opposing walls. Additionally, every multiple (‘octave‘) of this frequency get’s reinforced as well.
Let’s imagine that the rehearsal space mentioned before had the following dimension: 10′ x 9′ x 8’ (length x width x height). Also, let’s leave out the width and height of the room for now, for simplicity’s sake, and look just at the length of the room, which is 10 ft. To figure out, what frequency’s (f) wavelength (\lambda) fits right between this 10 ft, we can simply divide the speed of sound (c) by the distance:
f = \frac{c}{\lambda}In most situations, the speed of sound is a constant when we deal with sound inside, and we generally assume it’s 343 m/s, or 1130 ft/s. This then gives us the following equation:
113 Hz = \frac{1130 ft/s}{10 ft}Now, this is half-correct. The reason being is that the wavelength actually spans the entire distance (10 ft) and back (another 10 ft), so in order to find the lowest frequency that gets reinforced by a certain distance between two opposing surfaces, simply double the distance:
56.5 Hz = \frac{1130 ft/s}{(10 ft *2)=20 ft}56.5 Hz roughly corresponds to an A note—so whenever the bass guitar player from earlier plays an A during band practice, the rehearsal space would buzz.
Nodes and anti-nodes
Another interesting phenomenon with room modes is the ease of experiencing pressure differences when traversing the length (or the other dimensions) of the room. Let’s take the bass guitar player’s A note from earlier, and visualize this wave in a section cut of the room:
If you were to walk from the wall on the right towards the left wall, you would experience a pretty noticeable difference in the amplitude (perceived loudness) of the A note. Starting at the wall, it would be rather loud, as opposed to the very middle point between the two opposing walls: the A note would be significantly less loud, perhaps even barely perceivable. This concept is important to grasp, as it’s one of the most fundamental issues with critical listening environments (we’ll get back to this..).
Getting the complete picture
In the example above, we left out two out of three dimensions for simplicity’s sake. When we start taking these other two dimensions into consideration things get a little more complex. For sure, we can go ahead and use the equation above to find the corresponding modes for the width and height of the room as well. But this will still paint a very incomplete picture. The method above will only give us axial modes.
Axial modes are modes that resonate between two opposing surfaces, for instance between the front and back wall, or the left and right, or the ceiling and floor. Additionally, there are also modes that will form a complete ‘path’ between 4 surfaces, for instance between all walls before returning back to their starting point and reinforcing themselves; these modes are called tangential modes. It’s important to note, that tangential modes have half the energy of axial modes, because they hit twice as many surfaces (and thus, transfer energy while doing so). Lastly, there are oblique modes, which hit all 6 surfaces of a room before returning back to their starting point and reinforcing themselves. Oblique modes have half the energy of tangential modes—or a fourth of the energy of axial modes.
So, to sum it up:
- Axial modes hit 2 surfaces
- Tangential modes hit 4 surfaces, and have half the energy (or sound pressure) of axial modes
- Oblique modes hit 6 surfaces, and have a fourth of the energy of axial modes
Putting it all together
For the purpose of simplicity, when making a (quick?) theoretic assessment of a room’s modal activity, people sometimes entirely leave out tangential and oblique modes out of the equation (pun not intended..)—don’t be one of these people, as we need the entire picture to get a good sense of modal activity within a room. To do so, we can use the following equation (Rayleigh):
\frac{c}{2}\sqrt{\left ( \frac{n_{p}}{l} \right )^2 + \left ( \frac{n_{q}}{w} \right )^2 + \left ( \frac{n_{r}}{h} \right )^2}- c is the speed of sound
- l, w, and h represent the room’s dimensions
- n_{x} represents the number of frequency periods
Solving for this—increasing the harmonic integer (n) with every iteration—should give us a list of all modes that occur in this specific room. Of course, this can easily be automated, which we already did, so make sure to try out our room mode calculator!
How this is important
Above we mentioned earlier, being able to hear the pressure differences of a single mode when traversing the corresponding dimension is an important concept. Especially, when we’ve run the dimensions of our room through a room mode calculator and have ended up with a dozen or so modes between 50 Hz and 150 Hz, know that by simply walking around the room while harmonically rich sound is playing, you’ll be able to detect changes in amplitude across this frequency range. Essentially, this experience is very similar to changing the sliders on a graphic EQ: some frequencies get louder while others get softer.
In a perfect world, the sound pressure differences of the room’s modes would be as minimal as possible. This can be achieved by internal room acoustics such as absorption—there’s no other way of achieving this (changing the shape of the room simply moves the modes nodes to unpredictable points). This is where we at Calico come in, get in touch with us to see how we can help make your critical listening environment as linear as can be.