Blow across a bottle and it sings one clear note — and the emptier the bottle, the LOWER the note. The plug of air in the neck bounces on the springy air in the belly, a mass on a spring made of nothing but air. Its one resonant pitch depends on the neck, the volume, and the speed of sound. Slide the neck and tune the bottle.
A Helmholtz resonator is a cavity of volume V with a neck of cross-section A and length L. The slug of air in the neck (the mass) bounces on the compressible air in the cavity (the spring), resonating at f = (c / 2π)·√(A / (V·L)) with c the speed of sound. Wider neck raises the pitch, bigger cavity lowers it — the physics of every bottle, bass port, and ocarina. A fail-loud self-check throws unless enlarging the neck raises f and enlarging the volume lowers it.
The lumped mass-spring model holds when the wavelength is much larger than the resonator (low frequencies); it ignores viscous losses and radiation, and L needs an end-correction in practice. The √(A/VL) scaling is exact for the ideal resonator (Helmholtz 1863).