# The Helmholtz resonator, what's actually resonating?

I'm trying to more closely understand the physical mechanism behind the Helmholtz resonator.

If I model the resonator in terms of an analogous series linear electrical circuit: resistance ($R$), intertance ($L$) and compliance ($C$) I can write a transfer function in LaPlace operator, $s$ relating flow input to pressure output as

$$\frac{P}{Q}=\frac{(1/L)s}{s^2+\frac{R}{L}s+\frac{1}{LC} }$$

and this nicely agrees with many published formulations of the natural frequency in terms of the static pressure, volume of the resonator, length of the neck, area of the neck, etc. See one wiki here .

But in this relation I understand the inertance part is normally interpreted in terms of a straight tube, and I'm assuming it therefore does not apply to the the belly of the resonator - only its neck.

So my original conception of the Helmholtz resonator was that the entire volume of gas is going through a cyclic compression/relaxation. But given that the inertance is defined for a straight tube I'm realizing the mass of gas in the belly of the resonator is acting like a spring and the volume of gas in the neck of the resonator is acting like a (solid) mass. Thus acting together as a spring- mass oscillator. So its the plug of gas in the neck that's oscillating, driven by the gas in the belly -

Is that right?

Yes, the spring resonator seems to be the analogon of the Helmholtz resonator. You can also see it from the Helmholtz resonance frequency that depends on the square root of the ratio of the cross sectional area and the length of the neck: $$\omega_H = v \sqrt {\frac {A}{V_0 L}}$$ where $v$ is the speed of sound in air and $V_0$ is the cavity volume. Thus the Helmholz resonance is not a cavity resonance of the cavity volume.