In circuits oscillating at a single frequency, additional frequencies can emerge primarily due to non-linear components like diodes, which generate harmonics. Capacitors and inductors can also create resonances, allowing multiple frequencies to coexist. The discussion highlights a specific circuit using a transformer with three secondary coils and diodes, pulsed by a square wave, which results in an amplitude-modulated waveform. The interaction between the coils and their capacitance leads to resonant behavior, potentially explaining the observed additional frequencies. Understanding these interactions is crucial for effectively managing circuit behavior and achieving desired outcomes.