Thanks everyone for the input!
I agree that there are two noise components, one is structural through the body of my vehicle (this is an electric Mustang and we need the vacuum pump for the brake assist). and one is radiated through the sound wave which then sets off components around it.
To handle the structural issues, we plan to use a damping material like "B-Quiet". This material is a Butal and aluminum composite that will reduce noise transmission through structural components.
To handle the sound wave, we're using the Helmholtz Resonator.
As I understand it, while the speed of sound is in the equation, that doesn't preclude us from making a resonator that will reduce the noise. Once we find the dominant frequency of the noise, we can "T" a tube of x diameter and y length in the system before the vacuum intake. This should set up a standing wave that will cancel the noise of the wave made by the pump.
My issue is taking and analyzing the data to determine the noise frequency.
Someone mentioned the wave file. I don't know much about these files and how to set up the computer to take them. If I get a USB microphone, do I need an amplifier, is there a shareware program to record the noise? Once I have the file, I think I need to do a FFT (Fast Forier transform) on the file to get the natural frequencies. Does anyone know of any shareware that will do FFT's? Or at least something cheap?
Thank you all for your support!