I often see balancing subs used as a tool to mitigate modal issues at seating positions in a room. Either as part of the initial design or added later in an existing room as a countermeasure to fix a bad design.

But how does these frequency-limited balancing subs impact the modal distribution?

Let's take the example where a customer has two rows and two subs which plays down to 20hz. One center front and one center back to get rid of the 1st order length mode.

The 2nd row is placed in a 4th order length mode peak which affects the consistency. The frequency is so high that it can be fixed with smaller subs and hence the balancing sub question.

If two band-limited subs (50hz high passed, steep slope) are placed at each sidewall at 4th order length nulls, what will happen? I assume the 4th order length mode will be mitigated but how will that affect that original virtual sub which fixed the 1st order length mode?

Will there be a virtual sub in the room from 20-50hz and another virtual sub from 50-80hz? (Probably a third one around 50hz where they share content)

Looking forward to your comments - let me know if my question is not clear.