Appendix: Special Topics-Loudness

Table 1. CEA2010 Measurements for SVS SB12-NSD

(Data extracted from Audioholics Review, and Data-Bass)

A Method to Estimate Subwoofers In-Room Loudness

​If CEA 2010 measurement data are available, then the in-room design requirement can be converted to the same conditions as the CEA 2010 test and compared to the CEA 2010 measurement to determine whether a specific subwoofer can produce the desired in-room loudness.  The following describes a method that I have used. (Disclaimer: This estimation process has not been validated via actual in-room measurements. However, going through the process was somewhat educational. At the end of this article, two other estimation techniques are briefly discussed.) 

1. First, select the in-room peak loudness goal.  As stated above, many specifications define 115dB for LFE, but for this room, 105dB was chosen. 

2. Second, we need to start with some test data. CEA 2010 contains a couple of different tests. The most commonly used in reviews is the 2-meter ground-plane RMS test.  Each test can be run at various frequencies between 12.5 and 160 Hz. The most relevant frequencies for this estimation are 20/25/31.5 Hz. I chose 31.5 Hz because (I believe) there is typically little audio information below that frequency in movies and music. 20 Hz is another possible choice. It should be used if the requirement is for the subwoofer to play flat to 20 Hz, but it is more expensive to meet than 31.5 Hz.  

3. Next, we'll convert the desired in-room target loudness to the equivalent conditions of the CEA 2010 test.  If the subwoofer's CEA 2010 measured loudness exceeds the adjusted in-room target loudness, then the subwoofer meets the required loudness.

4. There are 4 adjustments to the in-room target volume.  These are:

   1. Room Gain: In the bass region (20Hz to 80Hz), Room Gain (aka Pressurization) increases bass loudness in smaller rooms. Without going into the physics of low frequencies, the subwoofer's energy stays within the room, effectively "amplifying" its output. Since CEA 2010 measurements are taken in an open field, translating the in-room response needs to account for this effect.

   2. Distance Loss: This is the same behavior as with speakers. The further away one sits, the lower the volume. In smaller rooms, we will be sitting closer to the subwoofer, so there is less loss. In larger rooms, the inverse-square law (Distance Loss) tends to a bigger factor. The CEA 2010 measurement conditions use a 2m distance, so again an adjustment to the in-room goal is needed to correlate the loudness.

   3. Boundary Gain: The CEA 2010 test conditions define a single ground plane test in an open area.  When a subwoofer is placed against a wall or in a corner, the sound is reflected into the room, increasing the volume (compared to the test data). This is called Boundary Gain. Mid-wall placement results in a theoretical 6 dB gain, and corner placement results in a theoretical 12dB gain. In reality, the gain is a couple of dB lower since rooms are never perfect.

   4. RMS to Peak Conversion: The CEA 2010 test data that is being used is an RMS test, but this estimate is for peak loudness; thus, this estimate needs to account for the 3 dB difference.

5. ​What we want to do is take the in-room target loudness (e.g., 105 dB) and subtract the various audio gains and losses to translate the target loudness into the subwoofer's volume under the CEA test conditions. In other words, we are translating the desired volume/loudness in a theater room to how loud the subwoofer would measure under CEA 2010 test conditions.  Then we can compare this translated target value to the CEA 2010 measurements of a specific subwoofer, and if the CEA measurements are louder (higher dB), then that subwoofer can meet or exceed the in-room target.​

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Boiling all the above factors into a single equation results in the following:

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Originally, this analysis was done for the room described on this website, but since then, the list of room sizes has been expanded, drawing from the room size definitions used by Audioholics.com.

• Small Rooms (< 1,500 cu. ft.) 

• Medium Rooms (1,500–3,000 cu. ft.) 

• Large Rooms (3,000–5,000 cu. ft.)

• ​Very Large Rooms (> 5,000 cu. ft.) 

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Then, for each room size, estimates were made for each of the four gain/loss parameters in the above equation. 

• InRmTarget - This is the target loudness goal for the subwoofer in the room. This value is the same for all room sizes. As stated previously, I used 105dB.  A worst-case value would be to use 115dB. 

• RoomGain - There are two ways to look at this value. One view is to use the room's volume as a reference. A doubling or halving of the volume changes the bass energy in the room by 6 dB. The very large room is assumed to have 0 dB gain; for large rooms, the base is boosted by 3 dB; for medium rooms, 6 dB; and for small rooms, 12 dB.  A second method is to use the pressurization frequency, i.e., the frequency whose wavelength is twice the room's length, and scale the gain accordingly, which yields results similar to the first method.

• DistLoss - The distance loss is the loudness (inverse square) loss due to the listener sitting more than 2 meters away from the subwoofer.  For very large and large rooms, the listener distance is assumed to be 4 m, which results in a 6 dB loss.  In the small room, the listening distance is assumed to be 2 meters, so 0 dB loss; in the medium room, it's in between, so 3 dB.

• BndyGain - It is assumed that the subwoofer is placed at a mid-wall location. This is treated as constant across room sizes, and since rooms are never perfect, this estimate uses 4 dB instead of 6 dB as stated above.  If the subwoofer were placed in a corner, then (in theory) 12 dB or a little less could be justified. 

• RMSConv - As previously stated, this is the conversion between RMS and Peak, so all rooms use the same 3dB.

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​​Table 2 consolidates the above information. The rightmost column lists the target CEA 2010 31.5Hz test results that a subwoofer needs to output to hit the target shown in the second-from-the-left column. ​​The SB 12-NSD measures 101 dB at 31.5Hz and thus meets the requirement for a medium-sized room. However, if the requirement were to meet the 105 dB target at 20 Hz or the 115 dB target, this subwoofer would not be powerful enough, and its low-frequency roll-off would start a bit too high for the tighter requirement.

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This table has not been verified by measuring subwoofers in the room, so its accuracy in the real world is debatable.

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Finally, a fair criticism of the loudness goals used here is that they are not chosen to yield a perfectly flat robust bass down to 20 Hz, and many bass enthusiasts strongly target achieving a flat response into the mid-teens. Furthermore, another valid criticism is that a full cinema reference volume was not the goal here.  With the described methodology to address these two criticisms, one needs only change the in-room target (InRmTarget), which will add 10 dB to the 2mGPTarget column in Table 2, and use the CEA 2010 20Hz data point for the selected subwoofer. 

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Table 2. Subwoofer Loudness Estimation

Note 1: In Small rooms, pressurization eliminates distance-based attenuation at 31.5 Hz.

Note 2: In Medium rooms, partial pressurization slows the attenuation rate.

Note 3: In actuality Room Gain is a Slope that begins at the room's pressurization frequency and increases as frequency goes down. Smaller rooms have a higher pressurization frequence, so there is more "room" for the gain to build up by the measurement point (31.5 Hz). Large rooms have a lower pressurization frequency (below 31.5 Hz) thus there is 0 dB of help at 31.5 Hz or 40 Hz. The table values approximate this by reducing room gain as room size increases.

Note 4: Adding a second subwoofer is estimated to add +3 dB to the output level. This assumes placement of two subwoofers on opposing walls. Co-locating the subwoofers changes this increase to +6dB. This lowers the target number by either 3 dB or 6 dB.

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Other Loudness Estimation Methods

There are a couple of websites that also describe methods for estimating, so it seems reasonable to mention them here.  The first is Audioholics.com, which has a nice description (HERE) of how they arrived at their approach.  The differences in the gain/loss items are:

1. A fixed listening distance of 4 m is used for all room sizes. Distance Loss is -6 dB for all room sizes.

2. Corner placement is assumed. Corner loading (+12 dB) is the same for all room sizes.

3. The reference level is 115 dB, except for the very large room, which uses 123 dB.

4. There is a room-size-dependent gain: +12 dB for small rooms, +6 dB for medium rooms, and 0 dB for large rooms.  

5. The room gain is subtracted from the original in-room target to obtain a room-gain-adjusted in-room target.

6. The Distance Loss, Boundary Gain, and RMS-Peak conversion, totaling 9 dB, is added to the subwoofer's CEA 2010 measurement at 31.5 Hz.

7. The adjusted in-room target (#5) is compared to the adjusted subwoofer CEA measurement. 

8. There is one additional criterion: a subwoofer's 25 Hz CEA measurement must be less than 6 dB below its 31.5 Hz measurement.

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The Audioholics estimation method uses the same four adjustments (Room Size/Gain, Distance Loss, Boundary Gain, and RMS to Peak) but combines them differently. The four adjustments are derived slightly differently and thus have different values.  Table 3 tabulates the parameters and specific values used in the Audioholics estimate.

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