Answer to Question #90119 in Mechanics | Relativity for Godwin

Question

the resonant frequency F of a closed air column is known to depend on the pressure and the density, p of the air and the length L of the air column. how are these quantities related?

Answer 1

The resonant frequency F of a closed air column:

$$F=\frac{v_{sound}}{4L}$$

At the same time:

$$v_{sound}=\sqrt{\frac{K_s}{\rho}}$$

Consequently:

$$F=\frac{1}{4L}\sqrt{\frac{K_s}{\rho}}$$

Where $K_s$ is a coefficient of stiffness, $\rho$ -air density, $L$ -length of the air column.