Mathematical definitions of all tube cavity vibration modes are developed from experimental results. The crossover from one mode to another is defined in terms of pertinent design parameters. A simple, accurate, and first time‐presented solution is developed for the spring‐mass vibration mode. The higher harmonics associated with the sping‐mass resonators, commonly called Helmholtz resonators, are identified from experimental data. Tube cavity limit conditions of zero length as well as zero and infinite volumes are included in this study. The resonance modes observed are spring mass, half‐wave, and quarter‐wave. Using the new solution for the spring‐mass mode, natural resonances are found to be bracketed by the limit conditions of the adiabatic and isothermal processes. The classical works of Von Helmholtz and Rayleigh concerning Helmholtz resonators is extended to include boundary‐layer theory, which theory was not introduced by L. Prandtl until 1904, a considerable time after the work of Von Helmholtz and Rayleigh.