Why a Large Diaphragm Microphone is limited to lesser frequency range
There are typically two reasons: First, a larger diaphragm is also heavier and hence it's inertia is bigger, which slows it down at higher frequencies (but also provides for significantly higher max SPL handling).

The main reason, however, is the relationship between wavelength and diaphragm size. The microphone basically "integrates" the sound pressure over the spatial area of the diaphragm. For a plane wave, the sound pressure is the same everywhere, but in a diffuse field that's not the case anymore. The wave length at 10 kHz is about 34 mm. So there are points on the diaphragm that are half a wavelength apart and it's entirely possible that one point sees positive pressure and the other negative pressure. These can cancel each other out (to some extent).