Resonant frequency of the room

More than you can eq out in some cases. Standing waves a general room mud in certain geometries can render a room almost uninhabitable (lol). Ever been in a bar that doesn't have music often and you can't hear make out someone sez and it just sounds like a muddled mess even though they have decent equipment? That's room resonance and stadia wave. Parallel ceilings and floors, square corners and no absorption can wreck a room.
 
I'm interested in how and to what extent the actual measured behavior of
the room has on the behavior of the speakers

The speakers don't care about the room, they always behave the same way.
If the woofer is very close to a surface, there could be enough reflected energy
to affect the driver to a small degree.
 
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how and to what extent the actual measured behavior of the room has on the behavior of the speakers
Thinking you are asking how much influence the room has on the end result.., assume that it takes over at lower frequencies. Location of woofer (including multiple locations) are a powerful tool. For example, trying to fill nulls with EQ is not appropriate.
 
Room mode calculator - online

Eq can only alter the direct sound from the speaker system, not the acoustical behavior
of the room.
amroc - THE Room Mode Calculator

Thank you Rayma, I found the link to have useful information - not just about room modes for my listening area, but also the raytracing tool that lets me see where the first, second, third reflections are bouncing from, which helps to determine acoustical treatment. Here are some screen shots:

First a Room Mode Calculator example"

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Next: A raytracing example (2 reflections) of my living room (not to scale)

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