Frequency response is an exact science and is related to the diameter (OD and ID) of the tube, as well as the material type and physical properties. There is an equation, called the Euler Bernoulli equation that allows one to determine resonant frequencies. Mass per length (ML) is a variable, as is Youngs Modulus (E).
Here is the equation (Den Hertog, P 432 mechanical vibrations) W = an*SQRT(E*I(MU*L^4))
f = an*sqrt(E*(pi*(OD^4-ID^4)/64/(MU*L))/2*pi
This will tell one, analytically where srong resonance peaks are.
Here is material data for 316 stainless steel
E = 1.93X10^11 N/m^2
Density = 8000 kg/m^3
Poissons Ratio = 0.26
We would need the axial and radial sound velocity, in meters per second, and the mechanical impedence to solve this equation. But there would be multiple frequencies where resonance would occur.
Changing material types can have an effect on resonance frequencies, as can changing the sound velocity. Thats why certain RPMs result in droning, and others do not. Take a look at cp-e nexus exhausts for designs that tune out resonance. For our application (FiSTs), 3" exhausts have a higher tendency to drone. That is why the MBRP exhaust says its a 3" diameter exhaust, but really isn't. This is to prevent droning. 409 is a martensitic stainless, as has a slightly lower density than 316 stainless. One is lower(409), and the other higher (316) density than regular carbon steel, used in aluminized exhausts. Lower densities increase resonance frequency response.
In the ducting systems I work on at my place of business, high speed vibration can cause fatigue failures, so we design all of our ducting with analytical vibrational analysis, which is verified by testing.
Me, I'm either going for the Cobb 316 or the Mountune, depending on the material and diameter.