Answer to Question #229335 in Physics for Any

Question

The resonance frequency f of a closed air column is known to depend on the pressure p, density of air and the length of air column l. How are these qua tities related.

Answer 1

$$f=p^a\rho^bl^c\\T^{-1}=(ML^{-1}T^{-2})^a(ML^{-3})^bL^c\\a=\frac{1}{2}\\b=-\frac{1}{2}\\c=-\frac{1}{2}\\f=k\sqrt{\frac{p}{\rho l}}$$