I have a unique situation, and have picked the brains of quite a few people, to no avail.

I have a Rheem Criterion gas furnace. Here is what happens:

Draft inducer initiates
Igniter (electric) lights up
Gas is fed through a minute later
All 4 burners light up simultaneously (for the most part)
All 4 burners start "pulsing" simultaneously (about 2 times per second)

When we first moved into the house the burners were smooth, but after a couple years this "pulsing" thing started. When I first noticed it, it would start slowly at first (about 1 pulse every 2 seconds) then smooth out. Then the pulsing would increase in frequency. Now it doesn't even smooth out, just a consistent 2 times per second. The furnace heats really well, cycles on and off accordingly. I'm just concerned about this "pulsing" thing. Any ideas?