Why is a double-membran mic more sensitive for sound from the side (90° and 270°, 4-6kHz)? For instance the polarpattern blows up to +3dB between 4kHz-6kHz.
A double-membran mic is in fact two cardiods back to back.
So let's look at a single cardiod.
The polar pattern of every cardiod mic is made up from two different effects:
In the lower frequency range:
Sound is mixed from those hitting the diaprags front directly and those going though the rear entry to the back of the diaphrag witch causes an opposite phase signal.
The rear entry damping elements lower the level of the sound to about 50%.
This way the cardiod is a 50% mix of a pressure gradient mic (fig. of eight) and a pressure mic (omni).
In the higher frequency range:
The rear entry acts like a low pass filter, few sound passes through the rear entry of the mic.
The mic acts like a pressure mic (omni).
If the size of the mic is the same or bigger as one quarter of the wavelength of the signal (high f.'s have a short wavelenght), diffraction causes a directivity to the front, like with any omni.
So in fact you have a "two way mic" with a frequency dividing network.
The x-over frequency lies in the range of 2-8 kHz, depending on size and construction.
The art of the designer of such a mic is, to couple the two ranges as smooth as possible.
It's impossible to achieve this absolutely perfect (same problem like with a 2-way loudspeaker).
Therefore most irregularities of cardioid mic's responses, specially in the polar pattern, happen to be in the range between 2-8 kHz.
For the double cardiod there is one more problem:
the diaprags are some millimeters apart, so signals aren't in phase, specially in the critical f. range.
This can lead to more problems in the capsule design and is a reason for the different frequency responses of the patterns of switchable double diaphragm mic's.
Regards
Kai