# Formula natural frequency double wall

I started with a book (pdf see here: https://www.pdhonline.com/courses/m104/m104_new.htm)

In this book there is the following formulla found $$f_0 = 170 / \sqrt{M_1 * t / (1 + M_1 / M_2)}$$. The page i refereing to is 4-2 (added below) but can also be found on this link(called page 28) http://buildingcriteria2.tpub.com/ufc_3_450_01/ufc_3_450_010032.htm
For text related to this figure see page 27 of the same link. I assume the situation it decibes is showed in situation B of figure 4-3 It is not a difficult formula but still i have some difficulties with it... The for here most importand one is as follows. When try to convert the formula to metric i run into a unit problem... So the unit version is as follows. $$f_0[1 / s] = 170[?] / \sqrt{[lb / ft^2] * ([ft] / 12) / (1 + [lb / ft^2] / [lb/ft^2] )}$$ With $$(1 + [lb / ft^2] / [lb/ft^2]) = [-]$$ and $$[lb / ft^2] * ([ft] / 12) = [lb / (ft * 12)]$$ resulting $$1/[sec] = 170[?] / \sqrt{[lb / ft]}$$ (i ignore the factor $$1/12$$ for now).
This would mean the unit (of the 170) of the numerator should be $$\sqrt{[lb/ft]} /s$$ while i would expect that it should be related to the speed of sound(and thus in $$ft/sec$$. The denumerator is would have $$ft$$ as unit).

So my question is as this: Where is this formula come from how is this formula build up. AND maybe a pointer to a paper where this formula comes from.

• What do you mean by double wall? What are you referring to? – FabioSpaghetti Aug 26 '19 at 15:40
• I assumed theformula and the text of the original link describing the situation of figure on the next page. Edit i figured out that i can link to single images... i try to insert them in the original text – Jan-Bert Aug 26 '19 at 17:43