Mass per unit length in Blevins formula for cylinder natural frequency

[GenSoft3d]

I came across this formula by Blevins for calculating the natural frequency of a hollow cylinder and was hoping that someone could answer a question I have for calculating the mass per unit length (m). Here's the formula:

f = A/(2*pi*L^2)*sqrt(E*I/m)

A= 9.87 for first mode
I = Area Moment of Inertia (m^4)
m= Mass per Unit Length (kg/m)


In this formula what equation should I use to determine the m (mass per unit length) for a thin-walled cylinder? Also, does I = pi/64*(d^4-di^4) in this case?

 

[GenSoft3d]

Does anyone have any insight on this? In the original data where I found this formula it states that "m = mass per unit length of beam (kg/m)". I take it that it's not referring to the mass density of the beam itself but rather the mass per unit length as described. If so then is this actually the area X the mass per unit volume (i.e., PI*d*t*density)?

As for the I (Area Moment of Inertia) I have found two formulas but can someone tell me which is the correct one to use for this application? Here's what I've found:

I = PI * (OD^4 - ID^4)/64

I = PI*d^3*t/8 (for a thin wall round tube)

Any help would be greatly appreciated.