If its a slow vibrating "sound" (3-5Hz) you are hearing, its a quite common "feature" of ANR's.
If had this with at least 3 different types including the Zulu. It's usually worst during taxi / runup and tend to disappear in the air. It also varies a lot from plane type to plane type.
I get it a lot in the RHS of a C172/P28 particularity when facing 90 degrees to the left (i.e looking at my student), but I never get it in the LHS on a multiengine regardless of where I face.
I think its just the ANR algorithm that can't handle slow RPM, or anything that sounds like slow RPM (like storm window noise). And also probably because the sense microphones on the ear-cups gets out of phase with regards to the sound source when you turn your head.
Its easily fixed on the ground by simple turning off the ANR until lineup
