An Acoustic Correlate: The Helmoltz Resonator

Figure 6: The Helmholtz resonator and its mechanical correlate.

• In the “low-frequency limit”, an open tube is a direct acoustic correlate to the mechanical mass.

• In the “low-frequency limit”, a cavity is a direct acoustic correlate to the mechanical spring.

• Using Newton's Second Law to model the air mass in the tube and Hooke's Law for fluids to model the compressibility of the air cavity, a sinusoidal solution can be found with natural frequency $\omega_{0} = c \sqrt{A/(L V)}$, where $c$ is the speed of sound in air, $A$ is the cross-sectional area of the tube, $L$ is the length of the tube, and $V$ is the volume of the cavity.