# How do harmonics travel through matter?

#### Exocomp

Joined Jul 25, 2023
3
Hi, I have a burning question regarding the nature of harmonics and sound. Specifically, I want to know the mechanism by which any given timbre of a musical instrument (or speaker) displaces atoms / molecules as it travels through space. I have a background in biology and chemistry but am weak with my physics so please bear with me. I'll try to articulate my question by using two examples though it may be difficult to understand what I am asking. I'm making assumptions here so please correct me along the way. I'll start with defining timbre as the fundamental + all harmonic content.

(1) Consider a pure sine wave with the fundamental frequency of 440Hz played on a speaker with no apparent harmonic content: I imagine the molecules of air moving back and forth in synch with the speaker because the pressure wave originated from the direct physical motion of the speaker. The air molecules undergo continuous compression and decompression in response to the wave front because they are coupled in 3D space. Since there is a single frequency, I posit the axis / orientation of the movement of molecules to remain static. This explanation seems simple enough to build on but may be flawed.

(2) Now consider plucking the A string of any old guitar with the fundamental frequency of 440Hz and random harmonic content: What is the motion of air molecules now? I speculate this could take one of several forms:

A - The timbre as a whole assumes a pseudo fundamental frequency that is an oscillation itself between the fundamental and all harmonics. Not only does the amplitude oscillate but the frequencies as well. I imagine this something like frequency modulation with the frequencies somewhat out of phase. The axis / orientation of air molecules remains static but their frequency changes with time.

B - Each atom has a specific frequency response. As the timbre travels through the air, the fundamental and the harmonics propagate in phase. I can't really get my head around what this would look like but I imagine it as some atoms oscillating in the X axis while others in the Y axis etcetera. The degrees of freedom (of each atom) are activated in phase in direct proportion to each (compatible) harmonic. This explanation makes more sense to me because each atom has unique spectral data and molecules assume different conformations.

I'm particularly interested in how molecular geometry changes (if at all) in addition to axis / orientation. So, this is a question about the waveform itself and matter's theoretical response. I understand what I'm asking is in the realm of advanced physics and chemistry so I may not get the answer I'm looking for. I prefer a mechanistic answer so don't spare the mathematics if necessary. Thanks for the help.

#### drjohsmith

Joined Dec 13, 2021
852
A big general question.

Any sound , is made up of many frequencies, of different amplitude and phase to each other
Fourier transform ,
https://en.wikipedia.org/wiki/Fourier_transform

harmonics are just a frequency , integer multiple of another frequency
they are no different to any other frequency
so we don't need to talk about harmonics, as they are just frequencies
https://en.wikipedia.org/wiki/Harmonic

Timber, is just a sound , as any other sound, and how its frequency / amplitude is
its just a sound like any other sound.
https://en.wikipedia.org/wiki/Timbre

Any sound at any point in time, is just an amplitude,
as amplitude changes over time, we perceive that amplitude change as frequencies.

Sound in air, is as you say "just" pressure changes,
in response to the amplitude.
and as pressure changes over time, we hear sound,

Pressure is just another way of saying a compression,

regarding transmission through a material,
be that a gas like air, or liquid like water, or a solid like concrete
remember at any one time and sound is just a bunch of frequencies at different amplitudes

so we can look at any material and see how a given frequency is attenuated / phase shifted to any other,
its a big vector,
and we can then put each and every frequency of the input sound, multiply it by the vector, and predict the sound on the output

Sound going through any material is just a pressure wave / compression,
be it at the atomic, sub atomic, crystal , boson particles or whatever level.

What else do you explicity want to knwo ?
suggestion, a single question is much more likely to get an answer than the broad brush stroke of your original question

#### MrChips

Joined Oct 2, 2009
30,983
Try not to overthink this question. There is not a lot of complex physics involved. There is no need to go down to the atomic level.

Sound originates as physical vibration at the source, whether it is a guitar string or loudspeaker, whether it is a pure sine wave or a complex waveform.

The vibration is propagated by whatever medium it encounters, whether it is a solid, liquid or gas. The only thing that changes is how each frequency is attenuated by the medium. In some cases, especially in solids, the medium may have its own resonant frequencies and hence can introduce its own set of frequencies as well as modify the amplitudes of the original frequencies.

For example, a vibrating string on a guitar has its own characteristic frequency and harmonics. When the guitar sound board is taken into account, an entirely different timbre is produced. Hence what you hear is a lot more that what originates from the vibrating string. Every guitar and violin maker knows this without having to implicate math and physics.

#### BobTPH

Joined Jun 5, 2013
9,174
It is all just variations in pressure. It would vary like a sine for a fundamental with no harmonics. When harmonics added, the shape of the wave is distorted, but it is still a single wave with a pressure at any point along it. The harmonics do not act on the air separately.

#### Exocomp

Joined Jul 25, 2023
3
Thanks for the insight but I'm not making myself clear. I want to know how each specific atom or molecule responds to the pressure wave(s). I'm referring to changes in conformation and axial rotation. When we speak of something oscillating, that can manifest in different physical ways. Something can be rocked back and forth in a linear fashion at 1Hz or it can be spun in a circle at 1Hz. Given that molecules have defined geometries, I would expect them to respond to different stimuli (lack of a better word) in a unique way. To my understanding, this is one of the major principles that spectroscopy and gas chromatography are based on. If you seen the video of the T shaped tool being spun at the space station, it is clear there are oscillations taking place that act in all 3 axis creating a very cool effect. This effect almost seems unreal because we are used to seeing oscillations in one axis.

As I said in #1 above, understanding the response is a lot more straightforward if we are talking about a single fundamental frequency. Since a guitar is a sum total of frequencies, I expect there to be all kinds of kinetic interactions taking place. I dreamed up a thought experiment to reword my question. I'm thinking of a real word scenario with a few small changes to make things manageable. Here's the scenario:

- A 440Hz note is stuck on a guitar in an open field with the detector (my ear) positioned a short distance away. Then a pure sine of 440 Hz is played on a speaker at similar amplitude and distance.

- The "air" contains only four molecules: O2 (linear geometry), N2 (linear geometry), NH3 (trigonal planar geometry) and (S,R)-1-Bromo-1-chloro-2-bromo-2-chlorobutane (2 stereocenter complex geometry)

- Each molecule of the same species is orientated in the same starting position.

It would be cool if someone could model the physical response of each molecule or provide the mathematical relationship. I hope this long winded response made my question clear. Thanks.

#### Exocomp

Joined Jul 25, 2023
3
Here is the video. Since sound is molecules smashing into each other, would the same kinetics apply to a pressure wave?

#### nsaspook

Joined Aug 27, 2009
13,435
0. 773m is the wave-length of a 440Hz audio note. At normal sound levels, analyzing 'air' or most acoustic interface materials at the microscopic level instead of the using the usually bulk macro scale seems completely pedantic when compared to spectroscopy and gas chromatography that do operate at molecular and atomic interaction levels.

#### drjohsmith

Joined Dec 13, 2021
852
Thanks for the insight but I'm not making myself clear. I want to know how each specific atom or molecule responds to the pressure wave(s). I'm referring to changes in conformation and axial rotation. When we speak of something oscillating, that can manifest in different physical ways. Something can be rocked back and forth in a linear fashion at 1Hz or it can be spun in a circle at 1Hz. Given that molecules have defined geometries, I would expect them to respond to different stimuli (lack of a better word) in a unique way. To my understanding, this is one of the major principles that spectroscopy and gas chromatography are based on. If you seen the video of the T shaped tool being spun at the space station, it is clear there are oscillations taking place that act in all 3 axis creating a very cool effect. This effect almost seems unreal because we are used to seeing oscillations in one axis.

As I said in #1 above, understanding the response is a lot more straightforward if we are talking about a single fundamental frequency. Since a guitar is a sum total of frequencies, I expect there to be all kinds of kinetic interactions taking place. I dreamed up a thought experiment to reword my question. I'm thinking of a real word scenario with a few small changes to make things manageable. Here's the scenario:

- A 440Hz note is stuck on a guitar in an open field with the detector (my ear) positioned a short distance away. Then a pure sine of 440 Hz is played on a speaker at similar amplitude and distance.

- The "air" contains only four molecules: O2 (linear geometry), N2 (linear geometry), NH3 (trigonal planar geometry) and (S,R)-1-Bromo-1-chloro-2-bromo-2-chlorobutane (2 stereocenter complex geometry)

- Each molecule of the same species is orientated in the same starting position.

It would be cool if someone could model the physical response of each molecule or provide the mathematical relationship. I hope this long winded response made my question clear. Thanks.
This is a very very broad question,
Id suggest that you will not get a thesis / doctorial presentation on this here, nor any one to do the "modelling the physical response of each molecule" as you ask for you

may be try a new single question, and as your knowledge expands, then try new seperate questions