The identified pitch of a sound is subjective. Other than a basic sine waveevery sound you hear is composed of multiple pitches in different mixes of loudness.
Pitch varies with the cycles per second (cps or Hertz or Hz) of the wave. Lets define our fundamental as the pitch “C” .
Double the Hz, so each since wave is half the original length, and you get a pitch which we call an octave higher, which is defined as the first harmonic. Let’s call that pitch “c” - the same note, but an octave higher.
If you add this to the original, you’ll hear a different tone quality, but you will probably still define it as sounding at the fundamental pitch of C.
Triple the Hz (so each sine wave is one third the original length) and you get not another octave higher, in-between. Musically, we’d call it “g”, and it’s the second harmonic of the fundamental C.
Add both harmonics to the fundamental, and the tone changes again.
The more harmonics you add, the harsher the sound appears.
If the harmonics don’t all start together, but each one is slightly delayed from the previous, the buildup of harshness sounds quite familiar - it’s very similar to what happens with a brass instrument, and sounds a bit trumpet or horn like. That’s because is a horn or similar instrument, the fundamental is the easiest frequency to get started, and the others take more energy to build up.
Yes, higher frequencies have more energy. That’s why microwaves can cook things.
I’m being simplistic towards the end, but the fundamentals are easy to understand. Sorry about the pun.