Parabolic reflector Equation

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Parabolic reflector Equation

Postby WeilandSmith » Fri Sep 18, 2015 6:58 am UTC


Short Question:

Where can I find equations for paraboloids? Specifically, regarding diameter of the disk vs frequency of the sound optimally emitted? Db levels would be a plus, but I can find those after.

Longer Explanation:

I hike a lot in Oregon, where the animals get pretty big. I'm trying to build a parabolic reflector dish for a non-lethal wild life deterrent. My research indicates that most of the dangerous animals have sensitive hearing around 30 kHz. I've seen some fixed sizes regarding the more common 200Hz - 16kHz range, but the db drop off with higher frequencies and I'm hoping a smaller disk will yield better results for my 30kHz needs.

I'm failing to find an equation to describe such a paraboloid.

What I'd like to hear is F(f)=xD where f is the frequency, x is the scalar multiple I'm looking for, and D is the diameter of a uniform paraboloid that never changes for a Parabolic reflector of mono-directional sound.

Wikipedia states: "A parabolic reflector type of loudspeaker must have a diameter twice that of the lowest desired wavelength, so to obtain directional control of frequencies down to 20 Hz, the dish would have to be over 50 feet (15 m) wide." This gives me hope, but I know better than to use wishful math.

My long term goal is to embed an off-axis parabolic reflector in the bottom of a short PVC pipe (for ease of use), so any equations for off-axis paraboloid slices would be nice. I stopped taking math classes around 3'd semester calculus, and hadn't taken physics. We didn't cover this yet and I haven't any college friends around since the move.

Thanks in advance. I miss physics teachers. They always entertain these questions.

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