Listening Room Acoustics: Room Modes & Standing Waves Part I

This article focuses on dealing with standing waves to improve bass problems for small room acoustics.  The best way both aesthetically and efficiency to solve bass problems is through modal manipulation using multiple subwoofers.  Once you reduce the seat-seat variance at bass frequencies, any remaining peaks can be EQ'ed out of the response to eliminate room resonances.  Low frequency bass traps can be used to supplement this solution if they are deemed to be necessary and practical.

For more information see:  History of Multi-Sub and Sound Field Management

As stated in an earlier article, room modes cause standing waves that can cause three acoustical problems:

• a level boost at some frequencies,
• an extent of the duration of sound at those same frequencies (resonance) and
• some profound dips at other frequencies.

These acoustical phenomena can produce resonant bass sound that has holes in it and suffers a lack of tightness. The sub’s frequency response will be greatly affected, but we should know that standing waves’ problems can extend to about 300 Hz.

Fig 1 Low frequency measurement in a typical listening room.

 

Figure 1 shows a low frequency measurement in a typical listening room. On the amplitude scale (the Y axis, labelled "level"), we can see a very irregular response. The time scale (the Z axis, labelled "time") is also very important. We can see that the resonances last a certain time. Some call this ringing. (Other rooms could easily exhibit longer ringing time.)

 

The standing wave

Have you ever sung in a bathroom? Some notes seem to make the whole room resonate. In fact, this is exactly what happens. This note you are singing is probably one of the room’s standing waves. Standing wave is a low frequency resonance that takes place between two opposite walls as the reflected wave interferes constructively with the incident wave. The resonant frequency depends on the distance between the two walls.

Fig.2 The reflected wave adds to the incident one.

 

The first standing wave frequency is given by:

f₁=c/2L

where L is the distance between the two walls.

c is the speed of sound

 

There will be many room modes between two walls as the phenomenon will repeat itself at multiples of the first frequency: 2f, 3f etc.

 

 

Standing waves pressure in a room

Let’s take a room whose one of its dimensions is 10’. Between those two walls, there will be room modes at:

f=56 Hz, 2f=112 Hz, 3f=168 Hz etc…

Fig 3 Distribution of the standing waves sound pressure level between two walls.

 

Figure 3 illustrates the distribution of the standing waves sound pressure level between two walls. One can note that:

 

• The sound pressure level is not equal in the room.
• The first resonance has near 0 SPL (sound pressure level) at the center of the space, the same for its odd multiples.
• The even multiples have maximum SPL at the center
• All room modes have maximum SPL near the walls.

 

This explains why the low frequency response changes as we change the listening spot in a room. It also explains why we have so much bass close to a wall.

Since there are three dimensions in a room, there will be three series of room modes.

 

	f Height	f Width	f Length
dimensions	8	13	19,7
f1	69	43	29
f2	138	86	58
f3	207	129	87
f4	276	172	116
f5	345	215	145
f6	414	258	174
f7	483	301	203
f8	552	344	232
f9	621	387	261
f10	690	430	290

Table 1 : The three series of room modes.

 

 

How to solve the problem?

The phenomenon is unavoidable; there are standing waves even in the best rooms. How to minimize the problem? One way is to distribute those frequencies in the spectrum so that they won’t be too close to each other; otherwise they can add up, if they are at high amplitude at the same place in the room, namely the listening spot. What’s more, they must not be too far away from each other because there can be an audible « hole » created in the frequency response. This is a rule applied even if we know that there will be holes in the frequency response, since all room modes are not heard at a single spot.

 

Influential factors to get a good distribution of those resonant frequencies are the volume of the room and its dimensions ratio. Gilford[1] states that the axial modes spacing should not be less than 5 Hz and not more than 20 Hz.

 

In smaller rooms, the Davis[2] frequency marks the superior limit from which modal density becomes high enough so there won’t be any coloration due to standing waves;

 

f=3c/L_min

where L_min is the smallest room dimension

c is the speed of sound

 

This rule is highly approximate. In an average size listening room, this frequency is around 350 to 450 Hz. The larger the smallest dimension, the lower this frequency is and, usually, the fewer problems we have.

 

 

Room analysis

Axial modes are issued from reflections on two surfaces. There are also tangential and oblique modes, which will be discussed later. Axial mode analysis makes it possible to identify the problems and to optimise the dimensions of the room in order to get a better axial modes distribution.

Here is a tool to do such an analysis:

http://www.hometheatershack.com/roomcalculator.xls.

Note: This calculator is used in the upcoming part of the article.

 

 

Large room or small room?

Here are two rooms of different volumes with the same ratio of dimensions.

 

	Room 1	Room 2
Size	Small	Large
Volume (cu ft)	860	1680
Dimensions (ft)	8 x 9,6 x 11,2	10 x 12 x 14
Dimension ratios	1 : 1,2 : 1,4	1 : 1,2 : 1,4

Table 2 Comparing two rooms with different volumes.

 

Using the calculator, when we enter the dimensions of the smaller room, we can see that there are several gaps of more than 20 Hz between modes. (see figure 4)

Figure 4 Axial modes for smaller room.

 

These “holes” can bring some coloration in the low frequency response. This is because smaller dimensions give higher frequencies, thus larger gaps between them. The situation is typical of small rooms and cannot be avoided. The same exercise done with the dimensions of the larger room shows less of such problems. (see figure 5)

Figure 5, Axial modes for larger room

 

In general, the minimum volume I recommend for a listening room is around 1500 to 2000 cu ft.

 

 

Axial analysis and correction of a typical room

Let us take a typical room for which a reader asked for advice; 8’ x 11,75’ x 18’ (2,44m x 3,6m x 5,5m). Room proportions 1 :1,47 :2,25 are very close to one reported by Louden[1] as being good; 1 :1,5 :2,20. Nevertheless, there will be three potential problems. By using the same tool as before (see figure 6), we can see that three pairs of modes may be problematic since their frequencies are too close to each other. (See also table 3)

Figure 6 Axial modes for 8' x 11,75' x 18' room.

 

 

Frequency	Following frequency	Difference
94 Hz	96 Hz	2 Hz
141 Hz	144 Hz	3 Hz
188 Hz	192 Hz	4 Hz

Table 3 Conflictual modes.

 

Changing one or two dimensions can solve the situation. To do this, we must determine which frequency belongs to which dimension. A table like the one in the calculator is necessary.

 

	Room Height	Room Width	Room Length
f1	70,63	48,09	31,39
f2	141,25	96,17	62,78
f3	211,88	144,2	94,17
f4	282,50	192,3	125,56
f5	353,13	240,4	156,94
f6	423,75	288,5	188,33
f7	494,38	336,6	219,72

Table 4 Calculated modes for the three dimensions.

 

On table 4, one can note that the problematic frequencies of 96 Hz, 144 Hz and 192 Hz are all related to the width. Those three frequencies should be a little bit higher to widen the gap between their precedents. If the width is slightly diminished (enter 11,33’ instead of 11,75’), the three problems have disappeared. (see figure 7)

Figure 7 Axial modes for 8' x 11,33' x 18' room.

 

 

Were those three frequencies a real problem?

First, let's say that the listening spot in this room is exactly in the middle. For the first conflict, 94 Hz is of the third order (odd multiple) (see table 4) and 96 Hz is of the second order (even multiple). So being of "opposite" amplitudes, they will not add up. The same for 141 and 144 Hz. On the contrary, 188 and 192 Hz could add together since they both are even multiples, that is at maximum pressure level at the center of the room.

 

In the second article of this two part series on standing waves, we will discuss:

• Axial, tangential and oblique modes
• The best dimensions ratios
• The Bonello criterion
• Solving standing wave problems

 

 

Michel Leduc
Acoustics professor, Cégep of Drummondville
Researcher in acoustics, Musilab, CCTT sound technologies
Acoustical consultant, SONART ACOUSTIQUE
Listening rooms and recording studios design
info@sonartacoustique.com

www.sonartacoustique.com

 

graphics courtesy of Ethan Winer and F. Alton Everest.

 

References

 

[1] Gilford, C., Acoustics for Radio and Television Studios. IEE Monograph Series II, Peter Perigrinus Ltd, London (1972) pp. 208

 

[2] Davis, Don, Sound System engineering, Third Edition, Focal Press, 2006.

 

 

[3] Louden, M.M. Dimension Ratios of Rectangular rooms With Good Distribution of Eigentones, Acustica, Vol. 24, (1971) pp. 101-104