# Rayleigh criterion for sound and parabolic microphone

Currently I am developing a parabolic microphone for a study project. I've heard and read that the maximum wavelength of sound that the given diameter microphone can focus is determined based on the Rayleigh criterion. However, I couldn't find any thorough explanation with sound-related formulas. Is that right? What is the formula for sound then? I know that it is also connected with diffraction limit.

• There are a couple of critical differences between acoustics and optics, especially in technical applications. In optics the approximation of infinite far field and plane waves is much more useful than in acoustics, where the performance near the ground (which in case of low frequencies is within a wavelength of the floor) is of importance. So while you may use the formulas from optics as a zeroth or maybe first order approximation, the actual performance of the device may vary considerably. What's your application? Dec 27 '14 at 18:32
• My application is a parabolic reflector focusing sound waves to a focal point. I would like to know how to calculate the minimum frequency (i.e. maximum wavelenght) that can be focused by a reflector of a given diameter. I am interested in rough approximation, very theoretical. I hope I adressed your comment appropriately. Dec 27 '14 at 18:36
• I understand what the microphone is supposed to do. My point is that what the device will really do depends very strongly on the geometry in which it will be used in. Are you trying to record birds or is it a technical application? Dec 27 '14 at 18:49
• Ok, so the device's geometry is: diameter - 0,5m depth - 0,125m focal length - 0,125m with the according cross-sectional parabola described by a formula y=(x^2)/50 Is this the geometry that you need? Dec 27 '14 at 18:51
• But are you using it 1m or 10m above the ground? Is this in free space or in a closed room? Are you recording a single frequency or a whole spectrum? Can you correct for its response? Would you be better of with multiple microphones and a phase sensitive setup? As I said, in acoustics these things matter much more than in optics. What is your ultimate performance requirement? Dec 27 '14 at 18:54