Helmholtz resonator: A cavity with a narrow neck behaves as a spring-mass oscillator. Air in the neck acts as a lumped mass m = ρ·A·L_eff; cavity pressure provides the restoring spring K = ρc²A²/V. This gives f₀ = (c/2π)√(A/VL_eff).
End correction: The effective neck length L_eff = L + 0.85r accounts for acoustic radiation from the neck opening, where r = √(A/π) is the neck radius.
Applications: Bass reflex speaker ports, car mufflers, architectural acoustics (cathedral side-chapels), guitar body resonance (f₀ ≈ 100 Hz), anechoic foam microstructure, noise barriers. The SPL response follows a second-order bandpass shape with Q = √(mK)/R.