Does electrical sawtooth wave actually produce sinusoidal oscillations at harmonic frequencies?

According to Fourier's theorem, we know that a sawtooth wave can be represented as a sum of sine waves. These sine waves we know as harmonics (in the context of sound). My understanding is that it is the same for electrical current.

Let us take a band-limited sawtooth wave in an electrical circuit. Say its frequency is 440hz. We know that its next harmonic after fundamental is $$880$$ Hz.

Do we actually have something oscillating in this circuit at frequency $$880$$ Hz in a sinusoidal waveform? What is it then? Or this is just a mathematical concept?

I am thinking from a perception point of view: when we produce a sawtooth wave by gradually increasing the voltage from $$-1$$V to $$1$$V and then dropping it from $$1$$V to $$-1$$V almost instantly. And that is what we see in the oscilloscope: spikes of $$2V$$ at $$440$$ Hz. But we don’t see its harmonics there. Do they actually happen or this is just an abstraction?

Please, help me with some guidance.

• Re, "a sawtooth wave can be represented as a sum of sine waves." Yes, because any periodic function actually is mathematically equal to its Fourier decomposition. Nov 16 '20 at 14:51
• You should check out D-class amplifiers. They convert audio into square wave pulses and reconvert them to audio by filtering the high frequency harmonics. Square waves are more power efficient to produce. en.wikipedia.org/wiki/Class-D_amplifier Nov 16 '20 at 17:06

No. The period of the waveform is $$1/440\text{s}$$.