Sorry, your understanding is mostly wrong.
- Sound is a pressure & velocity wave in a fluid medium, i.e. air.
- A human speaker will generate a 3 dimensional sound field around them. The sound pressure and particle velocity will be different at each location.
- A microphone measures the "sound" at one location. Depending on the type of microphone it either picks up the pressure, the particle velocity or a mixture of both. Let's stay with sound pressure to keep it simple.
- The microphone converts the local sound pressure into voltage. That is the signal that you see on the scope in the video.
- Human speech consists of different types of sound. There are three major types
- Voiced sounds. These are sounds that have an audible pitch. This includes vowels and nasals, such as "nnnn", "mmm", etc. Everything you can "sing" or "hum" to make a melody. They can be as long as you want.
- Fricatives: these don't have any pitch and are more like noise. Example "ssss", "ffff", "shshsh" etc. They can be as long as you want.
- Plosives: these are sounds that are short and just a single spike. "p", "k", "t" etc.
Your whole notion of fundamental + harmonics only applies to "voiced sounds", i.e. things that have a pitch. These can indeed be modelled by a fundamental and harmonics and, for example, the location of the harmonics determines whether a vowel is an "aaaa" or an "eee".
What you see on the scope is the sum of the fundamentals and the harmonics (and everything else: noise, reverb, air condition, ...). Technically it's not a wave, it's a signal.
Physically speaking: a wave is something that propagates over both over space and time.
The microphone has already resolved space, since it samples the sound wave only at one location and the dependency on space is lost. While it's still in air, it's a wave, but once it got picked up by a microphone it's just a signal. This is partially just "semantics", many people would still call it a "waveform" since it's a signal derived from a wave.
EDIT: answering the questions from the comments
(1) You speak of particle velocity; my understanding is that sound travels at 343 m/s in air. Are you saying this is not a constant, and that different waves/signals produce sound traveling at different speeds (lets say air is the fluid medium)?
No. Particle velocity and wave propagation speed are different things. Particle velocity is simply the speed with which air molecules wiggle back and forth. The higher the intensity, the more they wiggle and the higher the velocity. Wave propagation speed is constant and doesn't change with intensity. It's a function of the compressibility and density of the media.
(2) My understanding is that pitch is the frequency of a wave/signal;
No. Pitch is perceived. If a human can tell whether something is "higher" or "lower" it has pitch. For signals like sine waves and periodic signals, pitch correlates highly with the period of the signal. Other signals have no discernable pitch.
wouldn't fricatives and plosives (which are sounds) also have amplitudes and frequencies, hence, pitches?
No. They don't have pitches since they are not sufficiently periodic.
(3) What would be the correct definition for "fundamental" and "harmonics" here?
Any periodic signal can be expressed as a sum of the sine waves that are integer multiples of the fundamental frequency. That's the whole concept behind the Fourier series.
(4) when you say "What you see on the scope is the sum of the fundamentals and the harmonics..." what would you call this signal? Is there a special name for it?
Not really. It's just a signal.
(5) whatever the name of this signal is, I'm intrigued by your use of the word "sum" here; that its the "sum" of all these other things. Again, I would have expected each distinct "sound" to form its own signal on screen. Any chance you could elaborate as to how all of these things gets "summed" into a single signal?
I think you have it backwards. The sound signal just is what it is: it's air molecules wiggling back and forth and the microphone detects whether the pressure goes up and down. The concepts of fundamentals and harmonics (etc) can be used to analyze the signal or break it down into different components, but it's not the way it's generated or propagates. It's more of a math tool to make predictions and analysis easier.