# Wavelengths and Hearing

#### The Introvert

##### WORM
This is just a short question applicable to physics that I can't seem to find the answer to in Google.

Let's just say that a stereo emits a sound of frequency A, where the wavelength follows your typical sin curve like so:

It is my understanding that the wave reverberates back and forth, but if the sound was a single tone, the frequency would not change. So let's say then that the tone is a single unchanging tone, with frequency A.

Now the question is: what tone is it that we hear? Do we hear a single tone or do we hear either end (or anywhere in-between) at any given point? To express this by using the graph:

• Would be be hearing the 'tone' cutting through the graph, dissecting it in half, with a slope of 0? In this case, the line would run along the x-axis.
• Do we hear either end of the wavelength? In this case, the slope would still be 0 but would run along either y=-1 or y=1.
• Or, do we hear every possible combination of tones in the specific range (take any point in one unit [in this case one pi]) and we do not notice the reverberation (or our brains 'average' the sound and make it one single tone)? In this case, would we still be 'hearing' the line running along the x-axis with slope 0?
Which of these (if any) would be correct (or at least most plausible, if it is not answerable)?

I know this question may be confusing (because of my inability to properly ask a question I've been pondering), so please bear with me and ask questions if you do not understand.

#### walfin

##### Democrazy
You have not invited me but I am replying nonetheless.

The Introvert said:
where the wavelength follows your typical sin curv
The Introvert said:
but if the sound was a single tone, the frequency would not change.
I believe you mean that the wave is described by the sine curve, because if the wavelength varies according to a sin curve, the frequency would not be a constant since v=f*lambda and v can be assumed constant for the particular medium in which your sound wave is travelling.

The Introvert said:
Would be be hearing the 'tone' cutting through the graph, dissecting it in half, with a slope of 0? In this case, the line would run along the x-axis.
This does not make sense because sound is a longitudinal and not transverse wave. There isn't anything "cutting" through the wave because physically it is a line with the particles moving forward/backward along that line. Perhaps I misunderstand you.

The Introvert said:
It is my understanding that the wave reverberates back and forth
The Introvert said:
Which of these (if any) would be correct (or at least most plausible, if it is not answerable)?
For a sound wave that is reverberating (say, off a wall or something), you will hear the superposition of the two waves. I.e. sum of the curves.

#### Montresor

##### Banned
You're talking about something that was covered in 3rd year Adv. Perception (science psych.).

As far as I remember, option 3 is the most accurate*. Wish I could be of more service.

Remember that the stimulus is converted to electrical energy in the ... cochlea ...? and the impulses are transmitted via the auditory nerve with a frequency that corresponds to the frequency of the pressure wave in the air**.

Then a bunch of stuff happens and your brain integrates the information.and stuff

* Option 3 is out to lunch. I skimmed (sorry) and saw keywords like "average" and "pi" and I just assumed you meant integration from a purely mathematical standpoint.

** WRONG! As I remembered later after spending more time on the subject, post #36, the frequency of impulses roughly corresponds to the intensity of the stimulus, not to the frequency of the sound wave.

This carries important implications as we find the auditory nerve is actually the "cochlear nerve", with its nucleus receiving information directly from the surface area of the cochlear tissue, simply making it a sensory nerve. The axons would be sort of like a bundle of fiber optic cable, and would synapse at the medial geniculate nucleus (the thalamus is large and complicated ...), which then relays the information to the auditory cortex.

It stands to reason that this region of the thalamus would also be tonotopically organized, but perhaps if it wasn't it could lead to further understanding of its role.

#### SpaceYeti

##### Prolific Member
The frequency is what translates into pitch, tone. That is, on that graph, the distance between the waves's peaks. How high the waes are would be how loud the sound is, or the concussive power of the wave.

#### Montresor

##### Banned
The frequency is what translates into pitch, tone. That is, on that graph, the distance between the waves's peaks. How high the waes are would be how loud the sound is, or the concussive power of the wave.

Amplitude dude.

I believe the mystery we're trying to unmask is how the brain accepts the impulses and integrates them into the sound we perceive.

It's a known phenomenon that when you hear a pure pitch you can hear the oscillations, even though they happen what, like, thousands of times a second?

#### The Introvert

##### WORM
You have not invited me but I am replying nonetheless.
My apologies, I just invited a bunch of people that I thought would be interested in this. You are very much welcomed
I believe you mean that the wave is described by the sine curve, because if the wavelength varies according to a sin curve, the frequency would not be a constant since v=f*lambda and v can be assumed constant for the particular medium in which your sound wave is travelling.
Yes, that is what I meant. My physics lingo is not up to par.

This does not make sense because sound is a longitudinal and not transverse wave. There isn't anything "cutting" through the wave because physically it is a line with the particles moving forward/backward along that line. Perhaps I misunderstand you.
No, I think you understand me. I am concerned about the perception of the sound, as well as the physical construction of the wave, and how they may differ. So yes, the wave physically moves forward/backward along the line. However, are we hearing that shift, or or we hearing the 'invisible' line that would cut through the wave if it traveled as a straight line?

For a sound wave that is reverberating (say, off a wall or something), you will hear the superposition of the two waves. I.e. sum of the curves.
Yes, yes, I understand this. Although correlated, it is not of primal importance to me at the moment.

#### The Introvert

##### WORM
As far as I remember, option 3 is the most accurate. Wish I could be of more service.
What part of option 3? All of it?
Remember that the stimulus is converted to electrical energy in the ... cochlea ...? and the impulses are transmitted via the auditory nerve with a frequency that corresponds to the frequency of the pressure wave in the air.

Then a bunch of stuff happens and your brain integrates the information.and stuff
So your brain takes the wave and formats it into electrical energy, giving the perception of sound?

#### SpaceYeti

##### Prolific Member
Amplitude dude.

I believe the mystery we're trying to unmask is how the brain accepts the impulses and integrates them into the sound we perceive.

It's a known phenomenon that when you hear a pure pitch you can hear the oscillations, even though they happen what, like, thousands of times a second?
I don't think any of us knows enough about neuropsychology or physiology to try to answer that in any meaningful way. Though, were I to attempt it, I'd conjecture a straight transition from air particle reverberations into an electrochemical signal of the same properties; frequency and amplitude.

#### Hawkeye

##### Banned
are we hearing that shift, or or we hearing the 'invisible' line that would cut through the wave if it traveled as a straight line?
You are hearing the peaks of the wave as they coincide with the denser pressure of air that hits your eardrum triggering a response.

So your brain takes the wave and formats it into electrical energy, giving the perception of sound?
Yes.

And this is how...

#### The Introvert

##### WORM
This is almost exactly what the root of this thread is about.
On a side note, I play piano and I always used to hold down the keys without playing them in the upper register and would then play keys in the lower register to allow the keys in the higher register to vibrate and produce sound when I was little.

Anywho, you understand the question I'm asking, I think. How is it that all of those waves (technically speaking, an infinite amount of waves?) produce only one audible sound? Is the sound that we hear even a wave that is produced by plucking the string?

#### Montresor

##### Banned
a straight transition from air particle reverberations into an electrochemical signal of the same properties; frequency and amplitude.
^Once again, this process occurs in the EAR!

What's more, is I am telling you I possess the information. Not in my head, not in my database, not that I "get" it,

But it's in a binder somewhere in my basement.

#### Montresor

##### Banned
You guys have all missed the mark.

@The Introvert,

I can not accept that a simple demonstration of the processes that happen in the ear would satisfy your curiosity in this case.

#### The Introvert

##### WORM
I can not accept that a simple demonstration of the processes that happen in the ear would satisfy your curiosity in this case.
You are correct, it does not.

I think you may understand what I'm getting at here?

The underlying question, although it can be applied to this specific scenario, is of a much broader scope and of a much more important ilk.

#### Montresor

##### Banned
What part of option 3? All of it?

So your brain takes the wave and formats it into electrical energy, giving the perception of sound?
Sorry for triple posting guys, but I'm all wound up now.

Your brain accepts the electrical impulses via the auditory nerve. Bang. Then perception BEGINS. NOT-UNTIL-THEN.

The impulses correspond directly to the frequency produced in the air around your ear-drum.*

EDIT: Wrong again.
- This is the same thing I tried saying earlier, sort of before the concept of tonotopic organization was rediscovered.

#### The Introvert

##### WORM
You are hearing the peaks of the wave as they coincide with the denser pressure of air that hits your eardrum triggering a response.
So, our perception of the wave is only of the top peaks?

I'm confused.

What about the bottom peaks? Why aren't they registered? What about all the points in the wave in between peaks? Are those just thrown out? That doesn't make sense to me.

#### Montresor

##### Banned
The number of times the peak causes an impulse over a certain time period is what provides the frequency of the wave.

Cut and dry. That's all it does for you.

At the end of the day, as SpaceYeti said, there is more to sound than just frequency. Things like timbre (not in discussion here as we're talking unadulterated sine waves). Amplitude is another big one.

Your auditory cortex accepts this information and INTEGRATES (INTEGRATES) it into the sound we perceive.

#### Hawkeye

##### Banned
This is almost exactly what the root of this thread is about.
On a side note, I play piano and I always used to hold down the keys without playing them in the upper register and would then play keys in the lower register to allow the keys in the higher register to vibrate and produce sound when I was little.

Anywho, you understand the question I'm asking, I think. How is it that all of those waves (technically speaking, an infinite amount of waves?) produce only one audible sound? Is the sound that we hear even a wave that is produced by plucking the string?
Well, it is only perceived as a single audible sound. If you listen carefully to a low piano note, you can actually hear the overtones within it. Every note on the piano has a harmonic set of overtones. However they are much harder to identify in the higher octaves.

Also, the higher the overtone, the harder it is to pick out because it will be significantly quieter than the others within the series. The fundamental tone or lowest tone dominates in terms of aural perception.

Did you know if you cut off the the start and ending of the note, a flute and a violin sound pretty much identical.

Also, I tried to write a song using the harmonic series but as I played through the notes, I noticed a familiar tune

Damn you Strauss!!!

So, our perception of the wave is only of the top peaks?
Well, the peak is the catalyst for the sound. It is the thing that triggers a response from the eardrum to your brain. If your eardrum does not move, you hear nothing from the outside world. There are of course psycho-acoustics but that's a whole different ball game.

#### SpaceYeti

##### Prolific Member
^Once again, this process occurs in the EAR!

What's more, is I am telling you I possess the information. Not in my head, not in my database, not that I "get" it,

But it's in a binder somewhere in my basement.
Of course it happens in the ear. The part AFTER that is the mystery. If we're trying to answer how the qualia works, we need to solve the hard problem of consciousness first.

#### walfin

##### Democrazy
The Introvert said:
However, are we hearing that shift, or or we hearing the 'invisible' line that would cut through the wave if it traveled as a straight line?
We are hearing the shift. The eardrum vibrates. Hawkeye is correct. If the particles were stationary but in a "wave" displacement you would hear nothing.

So your brain takes the wave and formats it into electrical energy, giving the perception of sound?

The vibration of the eardrum would itself appear as the sound wave if plotted on an amplitude/time graph.

Montresor said:
Amplitude dude.
SpaceYeti said:
How high the waes are would be how loud the sound is, or the concussive power of the wave.
No, amplitude is volume. SpaceYeti is correct.

SpaceYeti said:
The frequency is what translates into pitch, tone. That is, on that graph, the distance between the waves's peaks.
That is the wavelength (loosely speaking, the distance between the peaks). The frequency is the "inverse" of that and is obtained by dividing the velocity by that. High frequency, low wavelength.

Technically, we should use the term displacement as distance is a scalar and cannot be negative.

#### The Introvert

##### WORM
Sorry for triple posting guys, but I'm all wound up now.

Your brain accepts the electrical impulses via the auditory nerve. Bang. Then perception BEGINS. NOT-UNTIL-THEN.

The impulses correspond directly to the frequency produced in the air around your ear-drum.
So, I think you're trying to point out that there is a transition from hearing to perceiving? I understand that; it's the same with seeing and perceiving - there's that gap (however small) in between your eyes collecting the light and your brain making sense of it. I have some pretty cool ideas about that, too, but it's for later

Anyway, I still want to focus on the actual part of the wave that is 'made into sense' by the brain. Surely it has to be the entire wave, and not just the peaks, as was suggested (or possibly misinterpreted by me)!

#### Montresor

##### Banned
Forgot to mention it relays through the thalamus (medial geniculate nucleus) first. I believe this region of the brain is sort of responsible for "buffering" the information to prep it for the cortex.

#### SpaceYeti

##### Prolific Member
So, our perception of the wave is only of the top peaks?

I'm confused.

What about the bottom peaks? Why aren't they registered? What about all the points in the wave in between peaks? Are those just thrown out? That doesn't make sense to me.
The peaks are the top. In the case of sound, it's actually waves of compressed air. The peak, then, is the center of mass for the zone of compressed air. How high the wave is, how compressed, determines volume, while the frequency determines pitch. That's... I don't see what else there is to say about it.

#### Montresor

##### Banned
I've since re-learned from that Wikipedia article that the primary auditory cortex is "tonotopically" organized, meaning certain physical regions can be shown to respond to a specific tone only.

Imagine small clusters of cells on the outer layer of your brain *(grey matter) that "light up". So there's A cells and B cells and C cells (A/B/C being auditory tones, corresponding to frequencies).

Some people have AC/DC cells.

Either way, imagine watching the surface of the brain light up bing bing bing as different tones are heard different areas would be responding.

Every area on the tonotopic map would correspond to a region of the cochlea that causes the initial electrical impulse. This concept is important because the same thing happens in the primary visual cortex. It is organized to reflect the surface of the retina (I believe). *retinotopic

I also believe if I am wrong somebody will say so.

OK so that's pretty simple.

Remember I stressed the importance of integration?

I believe that a second process occurs in --- let's call it the "secondary auditory cortex".

That is the topic for your research. The secondary auditory cortex.

* I wonder if there exists a wave function whose domain is equal to one wavelength and its range is Big Apple Pi's custom user title. Meaning a vertical asymptote at every "peak". I think this would most accurately represent an action potential in the nervous system, perhaps integrating this curve into a sine wave is possible?

#### The Introvert

##### WORM
Well, it is only perceived as a single audible sound.
Bingo.

It is perceived as a single audible sound. Think about that for a bit.

Now, I'll try to explain what I want answered here.

The sound as a physical body (the wave) is one of many (infinite?) waves.
We perceive that wave (via all the great ear stuff) as a single audible sound.
Where on the graph would the perceived single audible sound be?

Edit: Is that even a possible question to answer?

#### Hawkeye

##### Banned
The negative peaks (or troughs as I call them) on a sound wave aren't quite what you'd assume them to be. What the trough represents is the resting point of your ear drum.

#### Montresor

##### Banned
Anyway, I still want to focus on the actual part of the wave that is 'made into sense' by the brain. Surely it has to be the entire wave, and not just the peaks, as was suggested (or possibly misinterpreted by me)!

No you're missing the point again.

A new "wave" is created in the auditory nerve. A "wave" of electrical impulses. The original character of the sound wave is lost. It's broken down into smaller bits of data and then re-created in the processing center.

#### Montresor

##### Banned
You hear nothing without the oscillations!!!

You can't perceive an instant; every perception you have is a result of integrating bits of data that your brain receives over time.

That's perception bro.

#### walfin

##### Democrazy
The Introvert said:
Where on the graph would the perceived single audible sound be?
The whole graph is that single audible sound.

#### Montresor

##### Banned
No, amplitude is volume. SpaceYeti is correct.

I just saw this. Get bent. Volume and loudness are hardly different concepts. I was just giving him the word he was searching for.

#### The Introvert

##### WORM
The whole graph is that single audible sound.
Ack, this may have to do with the technicality of the graph.

Hawkeye said:
The negative peaks (or troughs as I call them) on a sound wave aren't quite what you'd assume them to be. What the trough represents is the resting point of your ear drum.
I was under the assumption that the troughs of the graph were just the lowest point in the vibration, and that the peaks were the highest point in the vibration, and that the average of these highs and lows (and everything in between) was what we hear (after extensive interpretation by our ears and brain). Apparently that isn't how it works...

#### Montresor

##### Banned
I don't know why but I'm really into this thread right now.

@The Introvert You seem to be ignoring my posts about the cortical processing, which is unfortunate as I believe this the information you were looking for.

Walfin keeps saying I'm wrong but he's not actually reading anything he just thinks I'm arguing with everybody, which I'm not, in fact.

For example, I'm not arguing with Hawkeye. Every single thing he has said so far has been correct. Do I have to acknowledge it? He's also talking about the ear drum, I'm talking about the auditory cortex receiving the information.

Maybe I am lost? I am talking about something different from everybody else here.

#### Hawkeye

##### Banned
Ack, this may have to do with the technicality of the graph.

Hawkeye said:
I was under the assumption that the troughs of the graph were just the lowest point in the vibration, and that the peaks were the highest point in the vibration, and that the average of these highs and lows (and everything in between) was what we hear (after extensive interpretation by our ears and brain). Apparently that isn't how it works...
If you punch a squirrel in the face 440 times per second, the impacts will generate a tone which is equal to the concert pitch note A.

The way you perceive sound is through registering the peaks (punches) of a wave (squirrel). The troughs are important as they provide the gap for the following peaks (more punches).

#### The Introvert

##### WORM
If you punch a squirrel in the face 440 times per second, the impacts will generate a tone which is equal to the concert pitch note A.

The way you perceive sound is through registering the peaks (punches) of a wave (squirrel). The troughs are important as they provide the gap for the following peaks (more punches).
Thank you! I was completely misunderstanding the graph that I presented.

Turns out that because of that, the underlying point has been demolished. The question I was going to ask is irrelevant in this context. I apologize for this, however, there is some very useful information in this thread!

It's getting late now, so I'll finish up these responses and log off, but thank you all for explaining this to me. I'll attempt to edit and re-ask my question in a manner that is represented by the actual question tomorrow sometime...

#### Montresor

##### Banned
If you punch a squirrel in the face 440 times per second, the impacts will generate a tone which is equal to the concert pitch note A.

The way you perceive sound is through registering the peaks of a wave. The troughs are important as they provide the gap for the following peak.
If you punch your eardrum 440 times per second you'll disturb the fluid in the cochlea which will localize its energy into one small area on the surface of the cochlear tissue (the 440 area), which will commence an action potential in the auditory nerve. This data will be transmitted through the medial geniculate nucleus in the thalamus where it is relayed through to the primary auditory cortex, where only one small region will be activated (the 440 Hz region). This information moves upward (bottom-up processing it's called - a technical definition) to the secondary auditory cortex where the individual packets of auditory data are rebuilt into a concept, what you perceive as an A, as in Highway to Hell.

A denser sound with multiple pitches will create a complex sine wave, wrought with interference. This will cause a response in many areas on the surface of the cochlea, thus it will cause a response in many areas in the auditory cortex, each representing one tone, which has been broken down by the cochlea and re-organized in the thalamus.

This is important:

The frequency of the nerve impulses becomes the intensity of the perceived sound, because it is originated in a tonal-specific region of the cochlea, plus it is a known fact that nerve impulses (action potentials) always have the same intensity with every event.

#### SpaceYeti

##### Prolific Member
I've since re-learned from that Wikipedia article that the primary auditory cortex is "tonotopically" organized, meaning certain physical regions can be shown to respond to a specific tone only.

Imagine small clusters of cells on the outer layer of your brain *(grey matter) that "light up". So there's A cells and B cells and C cells (A/B/C being auditory tones, corresponding to frequencies).

Some people have AC/DC cells.

Either way, imagine watching the surface of the brain light up bing bing bing as different tones are heard different areas would be responding.

Every area on the tonotopic map would correspond to a region of the cochlea that causes the initial electrical impulse. This concept is important because the same thing happens in the primary visual cortex. It is organized to reflect the surface of the retina (I believe).

I also believe if I am wrong somebody will say so.

OK so that's pretty simple.

Remember I stressed the importance of integration?

I believe that a second process occurs in --- let's call it the "secondary auditory cortex".

That is the topic for your research. The secondary auditory cortex.
Are there eight primary areas?

#### The Introvert

##### WORM
I don't know why but I'm really into this thread right now.

You seem to be ignoring my posts about the cortical processing, which is unfortunate as I believe this the information you were looking for.

Walfin keeps saying I'm wrong but he's not actually reading anything he just thinks I'm arguing with everybody, which I'm not, in fact.

For example, I'm not arguing with Hawkeye. Every single thing he has said so far has been correct. Do I have to acknowledge it? He's also talking about the ear drum, I'm talking about the auditory cortex receiving the information.

Maybe I am lost? I am talking about something different from everybody else here.
Your information is incredibly useful for me and I plan on digging through it tomorrow; it's late now, and the question I was trying to ask, although related to your material, is not exactly what I was getting at.

Let it be known that I'm not INTP (and thus not an overly analytical person), which is why my question was more broad-picture and less technical.

Edit: your posts on perception WERE getting at what I was trying to talk about, too. But the thread got hot really quickly and I'm tired and have work I actually should be doing so it kind of got lost in the multitude of posts here...

#### Montresor

##### Banned
I couldn't help it man I just started steamrolling. Like I said I did learn all this stuff in my 3rd year, which was 2008, so we're going on 5 years.

Anyways, the more I started talking about it, the more I remembered, and obviously I have no problems filling in the blanks with shit I make up.

Perception is an incredibly deep concept. Anyone who would label themselves a "deep thinker" would do well look a little further past the ear and really try to see what's happening with the "bottom-up processing" in the auditory cortex that I identified earlier, instead of just dismissing it, and simply accepting the fact that you just "hear" whatever your eardrum does.

I mean, come on.

#### Hawkeye

##### Banned
Mmm sounds like it's time for some Shepard Tones

If you get to the end, simply press start again to continue up the scale

btw, I agree with what you're saying Montresor.

#### SpaceYeti

##### Prolific Member
Perception is an incredibly deep concept. Anyone who would label themselves a "deep thinker" would do well look a little further past the ear and really try to see what's happening with the "bottom-up processing" in the auditory cortex that I identified earlier, instead of just dismissing it, and simply accepting the fact that you just "hear" whatever your eardrum does.
1) somebody may not consider themselves a "deep-thinker", and in fact consider the term a misnomer. For example, this guy. I don't think there's such a thing as a "deep" thinker, just a thinker who's entertained by figuring shit out. Some people aren't entertained by that. And, of course, there's always the "pseudo-intellectual" phase that any person goes through upon first pondering a subject.

2) While this subject is interesting, there's nothing wrong with admitting you don't know something. Nobody said "Hey guys, let's give up." I did say, however "I don't think any of us know this answer". That was all. I was wrong(ish). While you obviously knew more than I did, you still haven't answered the whole "qualia" problem... however, I also don't really consider the "hard problem of consciousness" to be an actual problem. The hard problem, I think, will be solved with the solution to the easy ones.

#### walfin

##### Democrazy
Montresor said:
Walfin keeps saying I'm wrong but he's not actually reading anything he just thinks I'm arguing with everybody, which I'm not, in fact.
Oh sorry I thought you were referring to the pitch. Silly me.

#### Montresor

##### Banned
It's ok @walfin I'm used to it, IRL. It seems a lot of times it doesn't matter what I say or what the subject is, the people around me are just like "no!". Sorry for grouping you into the "fucker" category, you don't belong there.

@SpaceYeti, the only part I took issue with is your plain assessment that nobody knows the answer. While you may not think I've got to the root of the problem, after sleeping on it, I still think that this whole concept doesn't even start to get "deep" until after the primary auditory cortex has registered the external stimulus. So you can appreciate my frustration that we can't even seem to get that far without going back to the start and talking about the ear drum again.

The OP specifically wanted to know what "part of the wave we are hearing".

This somehow became focused on "what part of the wave stimulates the ear drum".

My contention is that perception and sensation are different topics and no INTP should ever mix them up, regardless of ... well, anything.

The fact is, we are hearing the WHOLE WAVE. It's essential character is broken down (differentiation) into smaller packets of information which are re-built in the higher cortical processing areas (INTEGRATION) into the sound we hear. To really drive it home, I'll repeat that perception is a process that requires a time parameter to understand. We can not perceive an instant.

This is where perception psychology toes the line with philosophy, but we're not here to talk philosophy are we? We're here to talk science (spawn of philosophy).

#### Duxwing

##### I've Overcome Existential Despair
This is just a short question applicable to physics that I can't seem to find the answer to in Google.

Let's just say that a stereo emits a sound of frequency A, where the wavelength follows your typical sin curve like so:

It is my understanding that the wave reverberates back and forth, but if the sound was a single tone, the frequency would not change. So let's say then that the tone is a single unchanging tone, with frequency A.

Now the question is: what tone is it that we hear? Do we hear a single tone or do we hear either end (or anywhere in-between) at any given point? To express this by using the graph:

• Would be be hearing the 'tone' cutting through the graph, dissecting it in half, with a slope of 0? In this case, the line would run along the x-axis.
• Do we hear either end of the wavelength? In this case, the slope would still be 0 but would run along either y=-1 or y=1.
• Or, do we hear every possible combination of tones in the specific range (take any point in one unit [in this case one pi]) and we do not notice the reverberation (or our brains 'average' the sound and make it one single tone)? In this case, would we still be 'hearing' the line running along the x-axis with slope 0?
Which of these (if any) would be correct (or at least most plausible, if it is not answerable)?

I know this question may be confusing (because of my inability to properly ask a question I've been pondering), so please bear with me and ask questions if you do not understand.
The sine wave that you've mentioned actually represents the pressure oscillation that produces the sound, not the sound itself. The tone that you hear is the midline of the wave, and if only a single wave is present, then, in theory, you should hear only one tone.

-Duxwing

#### Hawkeye

##### Banned
The sine wave that you've mentioned actually represents the pressure oscillation that produces the sound, not the sound itself. The tone that you hear is the midline of the wave, and if only a single wave is present, then, in theory, you should hear only one tone.

-Duxwing
Urghh, I don't like averaging out sound waves. It seems so wrong and isn't something that should be dwelled upon. Sound represented as a longitudinal transverse wave is only useful when looking at frequency, amplitude, phase and timbre of a tone (although for the latter, a frequency spectrum graph would be more useful).

It should be noted that a single tone frequency is not something that occurs in nature. They are man made and are referred to as pure tones. They have no harmonic overtones and don't sound very pleasing on the ear.

#### Duxwing

##### I've Overcome Existential Despair
Urghh, I don't like averaging out sound waves. It seems so wrong and is something that shouldn't be dwelled upon. Sound represented as a longitudinal wave is only useful when looking at frequency, amplitude, phase and timbre of a tone (although for the latter, a frequency spectrum graph would be more useful).
Learn to cope, sir, learn to cope.

It should be noted that a single tone frequency is not something that occurs in nature. They are man made and are referred to as pure tones. They have no harmonic overtones and don't sound very pleasing on the ear.
Indeed.

-Duxwing

#### Hawkeye

##### Banned
Learn to cope, sir, learn to cope.

-Duxwing
It just seems like a pointless thing to talk about because it has no impact on anything; it's useless data.

Take the following tones for example.

If you took the average of each wave you would calculate different frequencies for each instrument. But they are all playing the same note - A at 440Hz

Averaging sound waves doesn't work.

#### Duxwing

##### I've Overcome Existential Despair
It just seems like a pointless thing to talk about because it has no impact on anything; it's useless data.
We can't understand those complicated tones until we understand pure tones. To analogize, one cannot understand chemistry without understanding atomic theory.

Take the following tones for example.

If you took the average of each wave you would calculate different frequencies for each instrument. But they are all playing the same note - A at 440Hz

Averaging sound waves doesn't work.
I have no real opinion on this matter, and I apologize if I appeared to express one.

-Duxwing

#### Hawkeye

##### Banned
We can't understand those complicated tones until we understand pure tones. To analogize, one cannot understand chemistry without understanding atomic theory.

-Duxwing
I was just trying to explain how interpreting a tone as an average of the wave is misleading. This isn't how sound works.

It would be more accurate to say that the tone perceived is a complete cycle of peak and trough.

#### The Introvert

##### WORM
The sine wave that you've mentioned actually represents the pressure oscillation that produces the sound, not the sound itself. The tone that you hear is the midline of the wave, and if only a single wave is present, then, in theory, you should hear only one tone.

-Duxwing
So then, in theory, the sound we hear (read: perceive) is running along the x-axis with slope 0?

Just double checking.

Perhaps my thought process is correct then...

So, to reiterate again: The pressure oscillation (sine wave) produces a sound (straight line) that splits the sine wave down the x axis with a slope of 0. Yeah, that's definitely what I'm thinking.

So how does that work then? The pressure from the peaks and troughs of the oscillation produces a stream of sound (air columns?) that beat at a certain frequency, giving pitch (for instance, 440 air columns produced a second would make the sound A)?