We observe that our experimentally measured emission power enhancement of a speaker inside a previously proposed metacavity agrees with our numerically calculated enhancement of the density of states (DOS) of the source-cavity system. We interpret the agreement by formulating a relation between the emitted sound power and the acoustic DOS. The formulation is an analog to Fermi’s golden rule in quantum emission. The formulation complements the radiation impedance theory in traditional acoustics for describing sound emission. Our study bridges the gap between acoustic DOS and the acoustic Purcell effect for sound emission enhancement.