The atomic entity of digital audio processing systems is a digital audio signal, i.e. a sequence of sound samples that represent the amplitude of a sound wave at discrete time intervals. Such signals are transformed additively, by combining them into more complex signals, and subtractively, by subjecting them to digital filters. In order to cover digital audio processing in a classroom from first principles, we need to form collections of samples in streams or arrays, and define operations on these collections in accordance with the constraints of digitization. In this work, we pursue an alternative approach, where the atomic entity is a continuous wave function. We present additive synthesis operations, including wave envelopes and musical abstractions in a purely functional setting. The final continuous wave function is digitized in order to make the sound audible. We report our experiences with what we call functional audio processing as an example domain for teaching functional programming to first-year students, where simplicity and conceptual elegance outweighs the inherent limitation to additive synthesis. We describe a sequence of teachable moments that highlight the potential of functional audio processing at an early stage in the learning process, before streams or arrays are introduced.