Animals produce a tremendous diversity of sounds for communication to perform life's basic functions, from courtship and parental care to defence and foraging. Explaining this diversity in sound production is important for understanding the ecology, evolution and behaviour of species. Here, we present a theory of acoustic communication that shows that much of the heterogeneity in animal vocal signals can be explained based on the energetic constraints of sound production. The models presented here yield quantitative predictions on key features of acoustic signals, including the frequency, power and duration of signals. Predictions are supported with data from nearly 500 diverse species (e.g. insects, fishes, reptiles, amphibians, birds and mammals). These results indicate that, for all species, acoustic communication is primarily controlled by individual metabolism such that call features vary predictably with body size and temperature. These results also provide insights regarding the common energetic and neuromuscular constraints on sound production, and the ecological and evolutionary consequences of producing these sounds.