How does the bass of speakers combine in a room?

What happens when you combine the bass response of two speakers? I'm referring to their real-world behaviour that you hear from your listening position, when all of their room-related peaks and dips are combined together?

We expect the bass level to be increased by 6 db. Do we actually get this much increase?

Do the peaks and dips average out? Or do they combine in a more complex way?

This chart shows two subs measured individually, with an average calculated response. This isn't the same as what you will measure if you measure them together. The response doesn't average out like this.

Peaks sum together. Dips don't subtract. Responses don't average peaks and dips. Where phase interference doesn't occur this will hold true and the combined response will be equal to or greater than the sum of all peaks.

Here you can see the measured response of two subs - left (green) and right (red) and the two combined (black). 

 

The shaded regions show where the left sub has a lower level (shaded green), or where it has a higher level (red). The combined response more closely matches that of the right sub where it is higher. The most obvious deviation is the peak at 44 Hz where the left sub has higher output. Below 25 Hz the behaviour changes and room gain appears to have some additional influence.

At the upper end of the modal range, we see some patterns more clearly. Here the combined response tracks that of the louder right sub even more closely. The dip at 100 hz remains because both subs have it, however the combined level is the lesser of the two. The dip around 140 Hz is eliminated completely because the flatness of the right sub dominates. The sharp dip at 160 Hz is also ignored as is the response of the left sub from 200 - 300 Hz where it is much lower in level.

In general, we can conclude:

• dips are not subtractive - they can be removed by adding another bass source that doesn't have the same dip
• peaks sum together
• the combined response of two bass sources is generally not an average, but it is more like the combined maximum level of the two

This has some implications in bass integration. The one that is of interest is that dips can be removed by adding bass sources together. These dips are best removed in this way rather than trying to use EQ. Bass traps are generally ineffective here.

Here is another example:

You can see the sub has a dip that the mains do not. The solution is to overlap the responses of both. So rather than crossing at 80 Hz, in this particular setup I ran the mains down to 60 Hz with a high pass at that point. The mains could in fact easily extend down to 23 Hz, however there was no need.