A standard sound-absorbent material has the optimum flow resistance - that is, it is harder than air and softer than wood. :^) You can blow through it with moderate effort, more like a pillow than a fiberfill comforter. It will absorb sound pretty well when the material is more than a quarter-wave thick. A wavelength at 1kHz is about a foot (34cm actually) so a 3" pad is good down to 1kHz. The memory foam I've seen is very hard or impossible to blow air through, so it would not be a good absorber.
That's from the simplest theory. Clever material designers can push this lower, maybe as much as an octave, by exploiting more subtle material parameters and/or non-uniform materials. And a thinner pad of higher resistance will absorb less energy but do it down to a lower frequency.
I have left out bass traps which get to much lower frequencies but only in a more narrow frequency range, by exploiting resonances.