Studio Acoustics Part 2: Standing Waves

This mini-series sees Joe Albano demystifing the science of studio acoustics. In Part 2 we look at low-frequency standing waves which can get in the way of getting a well balanced mix.  

In the first installment of this series, I outlined a number of room acoustics issues that can get in the way of achieving good recordings and mixes. In this article, I’ll start going over the specifics, beginning with one of the most common causes of problems with getting a good mix balance, and the ability of a mix to “travel” well—to sound good in other locations. That issue is low-frequency standing waves.

Stand By Me

Whenever sound waves occur in an enclosed space, they interact with the room boundaries—they can either reflect off them, be absorbed by them, or pass through them. Standing waves, a.k.a. room modes, are a function of reflected waves. When mid and high-frequency waves bounce around a room, they can either result in a pleasant sense of ambience—liveness—or cause unpleasant artifacts, like flutter echoes. But when low-frequency waves reflect off room surfaces, they manifest themselves a little differently.

Fig 1 A typical Studio Control room layout

Fig 1 A typical Studio Control room layout

Without getting into the physics of it too much, all audio waves have a particular fhrequency—the rate of vibration of the sound-producing object, measured in vibrational cycles-per-second, or hertz. The wave itself is a series of air pressure variations (higher than normal pressure—compressions, and lower-than normal pressure—rarefactions), that emanate out from the source and propagate through the room. When one of these waves meets a room surface (wall, floor, ceiling) it will reflect back into the room, bouncing from surface to surface. At mid and high frequencies, this can be subtle, but low frequencies present a different case, because of their wavelengths.

The Long and Short of It

Every wave has a wavelength—the physical distance that wave travels in the room is the time it takes to complete one cycle of vibration. Since low-frequency waves vibrate more slowly than mids or highs, their wavelengths are longer. Mids and highs may have wavelengths of anywhere from a few inches to a few feet, but lows often have wavelengths that approach and exceed the room dimensions themselves. When such a wave reflects between two parallel surfaces in a room, it doubles back on itself, causing interference, in the form of reinforcements and cancellations, at the particular frequency associated with that wavelength. 

When this happens with mids and highs, these cancellations and reinforcements are distributed throughout the room. However, with longer, low-frequency waves, the cancellations and reinforcements are localized to specific areas in the room. The result is that the bass response of the room is uneven at certain frequencies—there will be too much bass at a particular frequency in some spots in the room, and not enough at others.

Fig 2 Standing Waves reinforcing and canceling a particular frequency and its Harmonics at various locations in a room

Fig 2 Standing waves reinforcing and cancelling a particular frequency and its harmonics at various locations in a room

If the engineer/mixer, or a speaker, is in one of these spots, then the sound heard in the room will be a false picture of what the recording’s low-end is really like. Typically, this leads to EQ decisions that compensate for that one room’s low-frequency issues, rather than for actual issues in the recording itself. When the resulting mix is heard in other rooms, which don’t share those exact same low-frequency irregularities, they sound bad—uneven low end, either too thin or too tubby, overall.

Mapping it Out

To deal with this issue, the first thing thing that must be done is to determine what frequencies and what locations in a given room will be affected. Fortunately, for a particular room, the specific frequencies at which standing waves will occur, and the locations of the problem areas, can be calculated based on the dimensions of the room. I’m not going to go through all the physics formulas for this—there’s no room here, and they can be found in any number of books on studio acoustics—but I will mention one or two of the most basic calculations that can be done. 

Standing waves occur between all parallel room dimensions—walls (length and width) and floor & ceiling. There are three types—axial, tangential, and oblique modes. The only ones that can really be determined easily are axial modes, and they’re usually the most prominent—the most problematic—so I’ll only cover them. 

When the wavelength of a particular frequency is exactly a multiple of a room dimension, a standing wave will occur at that frequency. Additionally, since complex musical waves all have harmonics, which are multiples of the fundamental frequency, then the harmonics’ wavelengths will also be multiples of the same room dimension and will also result in standing waves. But the cancellations and reinforcements for each harmonic’s standing wave will occur at different spots in the room. 

Don’t Fear the Formula

This can be calculated and mapped out—without any need for test equipment or special physics knowledge—with the simple formula 1130÷2L (where 2L = room dimension x 2, and 1130 is the speed of sound). This gives you the frequency at which a standing wave will form in that room—standing waves will also form at whole-number multiples of that frequency (the harmonics). 

The frequencies of all the standing waves will have reinforcements at both walls—these are called antinodes. The primary standing waves will also be have a cancellation—a node—halfway between the walls. The next harmonic’s standing wave will have cancellations—nodes—a quarter of the way out from each wall, with antinodes in between. The third harmonic will have alternating nodes and antinodes a sixth of the way from each wall. The diagram in Fig 3 shows how these first three standing waves affect the balance in the room at those frequencies. Audio example 1 is what you might hear if you walked from one wall to the opposite wall in a room with standing waves.

Fig 3 The distribution of the Nodes and Antinodes of the first three (of one set of Axial) Modes in a room.

Fig 3 The distribution of the nodes and antinodes of the first three (of one set of axial) modes in a room.

Audio example 1 How standing waves affect the sound: A repeating bass part is heard, while the listener gradually walks from one wall, through the center of the room, to the opposite wall; the tonal variations heard are due to the nodes & antinodes, as shown in Figs 2 and 3.


The first three or four axial modes, at the lowest frequencies, are usually the most problematic—above 300 Hz or so the nodes and antinodes are so close together that they average out for a more even response at those higher frequencies. But remember, these nodes and antinodes occur for each of the three parallel room boundaries—length (front & back walls), width (side walls), and height (floor & ceiling). 

What to Do

While it’s easy enough to determine where in the room the response may be the most uneven, fixing the problem can be a bit more challenging. Commercial solutions include a variety of products, like bass traps, that are placed against walls, or, more likely, in corners, to break up the standing waves, and restore a more even balance to the space. These must be “tuned” to the particular room, so the companies that sell them usually provide a way for their customers to enter room data, which is used to calculate the best products at the correct sizes to deal with that particular location. 

If you’re involved with the initial construction of the recording/mixing space, from the beginning, then cavities can be designed into the walls themselves to counter the effects of standing waves. This does require a bit more math & physics, though, again, the methods and calculations are well documented in a number of books on studio acoustics. The biggest drawback is that some square footage will need to be sacrificed to allow for effective treatment.

The Golden Mean

One way to minimize the negative effect of standing waves is to construct a room with a set of what’s called “golden mean” dimensions. These are specific combinations of width, depth, and height that insure that there won’t be any overlap of (at least axial) standing waves between those three dimensions at which they form, and that the nodes and antinodes that do develop are spaced in the room so as to not interact with each other, and balance each other out, for an acceptably even low-end response throughout the room. This means no surface dimensions that are multiples of each other—a room that’s 24’L x 16’W x 8’H would not be ideal, because 24 and 16 are multiple of 8, so harmonics of one set of standing waves would coincide with different harmonics from the other(s), making the low-frequency unevenness two or three times worse. A cube would be the worst possible shape! Some traditional golden mean dimensions are listed in Fig 4.

Fig 4 Some established “Golden Mean” room dimensions

Fig 4 Some established “golden mean” room dimensions

The Standing Wave Shuffle

Even if you don’t have the option to apply any of the treatments mentioned, the least that can be done is to insure that the engineer/mixer’s “sweet spot”—the primary monitoring position—and the locations of the speakers, are not right in the middle of a node or antinode. That means that having the speakers up against a wall is probably best avoided, unless those speakers are specifically designed for that placement. Even though the bass response may have less oomph with a console or desk-top placement, the low end will likely be more even, and that’s much more important than bone-rattling bass. If you map out the positions of the strongest standing waves, as in Fig 5, you can position the sweet spot in-between nodes and antinodes—while this doesn’t eliminate the problem, it will provide a more even reference for mixing.

Fig 5 Top) A studio with speakers and engineer/mixer’s “Sweet Spot” coinciding with standing waves Nodes & Antinodes (problematic); Bottom) The speaker position and “Sweet Spot” relocated to avoid the Nodes & Antinodes of the most prominent standing waves (better)

Fig 5 Top) A studio with speakers and engineer/mixer’s “sweet spot” coinciding with standing waves nodes & antinodes (problematic); Bottom) The speaker position and “sweet spot” relocated to avoid the nodes & antinodes of the most prominent standing waves (better)

Most important, you need to get to know the sound of the room, so as not to make EQ choices that will only be valid in that room, and will make a mix sound worse everywhere else (Audio Example 2).

Audio Example 2 A 4-bar passage is repeated 4 times: A) The original un-EQ’d mix, as it would be heard in a room with no standing wave issues; B) The same mix as it might sound in a typical room with an uneven low-frequency balance from standing waves; C) EQ applied to compensate for the room imbalances; D) What that mix might sound like when heard in a different room, that doesn’t have the same standing wave imbalances


To do this, assemble a collection of good, commercial recordings, and use them to get to know how the low end sounds in your room with mixes that are known to have a proper low-frequency balance. Then use that as your reference for what the low end balance in your own mixes should sound like in your room, and, whenever possible, check your mixes on other systems, in other rooms, before finalizing them. It’s certainly possible to make good, well-balanced mixes, even in a room with a less-than-perfect response due to standing waves issues, as long as you know the room well enough to not let it trip you up.

Next time, I’ll continue this series with a look a mid-and high-frequency reflections.

Joe is a musician, engineer, and producer in NYC. Over the years, as a small studio operator and freelance engineer, he's made recordings of all types from music & album production to v/o & post. He's also taught all aspects of recording and music technology at several NY audio schools, and has been writing articles for Recording magaz... Read More

Discussion

Jabun
Good article, though you should give units for the values in the formula, otherwise it won't work properly. The speed of sound is 1130 ft/s as you give it, so the room lengths will have to me measured in feet to get the correct frequencies.

Alternatively, you could go metric by using speed of sound = 344 m/s, then your room lengths would need to be in meters.

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