ShotGunMike.pdf

I am not sure about audio, but for electromagnetic waves, the simple diffraction rule of thumb is that the half power beam width is about wavelength/diameter radians. Thus with a wavelength of 1 m and 0.6 m diameter, we are talking about something like 100 degree capture angle.

Such an paraboloid has a capture area of about 0.3 m², thus at 120 dB SPL (1 W/m²), the audio power at the microphone would be about 0.3 W (+25 dBm). Find out the microphone conversion efficiency and you can calculate how much power is delivered to the amplifier.

A good amplifier at room temperature will have a thermal noise density of -174 dBm/Hz, thus at 20 kHz bandwidth, the noise power is -131 dBm.

From these figures, you should be able to calculate the audio level required for a specific SNR or alternatively calculate what SNR is obtainable at a specific audio level.