Thinking about that analogy makes my head hurt.
Here is another "real world" example.
I have 2 sine waves-both of equal amplitude.
But when I turn them both on, the result get larger and smaller-depending on how the phase relationship of the waves is.
This was done on an old CRT scope-so that is why some of the traces are not "complete". You are just seeing what is being traced on the screen at the time the shutter on the phone is open.
But you should get the idea.
You can easily see how the higher freq wave is "riding" on the low freq wave and how the low freq wave is pushing the HF wave much higher in level (as in JRs example of a boat)
If the amplifier does not have enough voltage swing (power), it cannot reproduce the HF signal-resulting in distortion.
The top 2 photos are the individual freq. Both are clean
The bottom left is when they are added together-with plenty of headroom on the amp.
The bottom right is when each signal is just a little under clipping. So when they are added together, you end up with a greatly clipped signal.
If the lower freq signal was filtered out, then the higher freq one would still be nice and clean.
NOTE: I did readjust the gain on the scope channel to make it fit onto the screen.
In the first 3 photos, no gain was adjusted.