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Topic: Help me understand why sound is one dimensional (Read 12516 times)
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## Re: Help me understand why sound is one dimensional

##### Reply #50 – 2018-07-19 01:55:41
space is not a dimension ?

A location in space can be described with three dimensions, and space/time (in certain circumstances) 4 dimensions.  However, the number of dimensions for a sound pressure measurement is scalar pressure + time.  One can mix multiple pressure measurements (along with other intelligence in the data -- incl spatial location of the measurements), then allow the sound to help describe the environment (including the source locations.)  This description of the environment is what sonar does (and how the brain calculates the spatial relationships.)

John

## Re: Help me understand why sound is one dimensional

##### Reply #51 – 2018-07-19 18:44:53
space is not a dimension ?

A location in space can be described with three dimensions, and space/time (in certain circumstances) 4 dimensions.  However, the number of dimensions for a sound pressure measurement is scalar pressure + time.  One can mix multiple pressure measurements (along with other intelligence in the data -- incl spatial location of the measurements), then allow the sound to help describe the environment (including the source locations.)  This description of the environment is what sonar does (and how the brain calculates the spatial relationships.)

John

Are you a vacuum cleaner designer ?
(The smallish high RPM motors embedded in the dyson appliances are horribly noisy and is a real pain to endure)

A mathematician should think about the Inverse-square law, no ?

## Re: Help me understand why sound is one dimensional

##### Reply #52 – 2018-07-19 19:06:23
space is not a dimension ?

A location in space can be described with three dimensions, and space/time (in certain circumstances) 4 dimensions.  However, the number of dimensions for a sound pressure measurement is scalar pressure + time.  One can mix multiple pressure measurements (along with other intelligence in the data -- incl spatial location of the measurements), then allow the sound to help describe the environment (including the source locations.)  This description of the environment is what sonar does (and how the brain calculates the spatial relationships.)

John

Are you a vacuum cleaner designer ?
(The smallish high RPM motors embedded in the dyson appliances are horribly noisy and is a real pain to endure)

A mathematician should think about the Inverse-square law, no ?

Not directly related to Sir James Dyson, however I did recently mention his gathering of the dyson.com domain early in the Internet, therby frustrating my own ability to get it back then :-).  I am of much less noteriety -- only writing a part of the early FreeBSD kernel code and doing various interesting things at Bell Labs many years ago.  Most recently, working on audio processors including a fully functional DolbyA decoder -- (some interesting things now happening in that realm.)  Basically, just a geek.

Regarding the inverse-square law -- that can certainly be part of the calculation used to help determine information about the environment given multiple scalar sound measurements vs. time.

John

## Re: Help me understand why sound is one dimensional

##### Reply #53 – 2018-07-19 21:20:12
environment given multiple scalar sound measurements vs. time.
John

I don't understand "scalar" part of the sentence, you mean that we can vectorize the sound propagation with a microphone array... how ?
It can only be performed in the far field IMO (if it is possible)

## Re: Help me understand why sound is one dimensional

##### Reply #54 – 2018-07-19 21:30:05
environment given multiple scalar sound measurements vs. time.
John

I don't understand "scalar" part of the sentence, you mean that we can vectorize the sound propagation with a microphone array... how ?
It can only be performed in the far field IMO (if it is possible)

I am not saying how (by what method), except that information about the environment can be inferred by using multiple sensors.  A single sensor with no other information would only provide 1 dimension of data.  Perhaps the distance between two impulses can be measured -- but what is the reference point of the two?  SO, one sensor basically gives you the ability to detect sound at that point only (no directional information.)  With multiiple sensors, things like reflections and signal intensity can start to be used to guess better at directions.  I am not claiming exactly what kind of data about the environment that can be figured out.  For example, a lot of information can be figured out about earthquakes by simply listening -- not even pinging of any kind.  By using more sensors -- more kinds of information (dimensions) can possibly be derived.  By explicitly adding a controlled source of some kind, even more information might be able to be obtained. (or, maybe with a controlled source of some kind, the precision might be greater.)

## Re: Help me understand why sound is one dimensional

##### Reply #55 – 2018-07-19 22:23:23
IMHO the 1D point of view don't conceptualize the reality because all audio measurements are performed by people who have the sound field in mind.

## Re: Help me understand why sound is one dimensional

##### Reply #56 – 2018-07-19 22:40:46
IMHO the 1D point of view don't conceptualize the reality because all audio measurements are performed by people who have the sound field in mind.

If a person has a picture of what they expect the sound field to be -- and then uses a singular real data point, aren't they really sustituting 'fake' (not necessarily invalid) effective data points for real ones?  No matter what you are imagining, there has to be some kind of framework -- and in space, there are normally 3 dimensions.  One can abstractly create more dimensions for some kind of analysis purpose, but in reality there are three dimensions in space.   Adding more dimensions isn't just describing space, but rather some kind of hyperspace (no scifi here.)

John

## Re: Help me understand why sound is one dimensional

##### Reply #57 – 2018-07-20 01:16:01
If a person has a picture of what they expect the sound field to be -- and then uses a singular real data point, aren't they really sustituting 'fake' (not necessarily invalid) effective data points for real ones?
The more data points the better which, as I recall, is kind of why we moved from mono to stereo back in the 1950's.

But please note that your ears have only two data points, yet you are able to hear a three dimensional sound field.  If two ears can do it, why can't two microphones?

Ed Seedhouse
VA7SDH

## Re: Help me understand why sound is one dimensional

##### Reply #58 – 2018-07-20 03:59:50
If a person has a picture of what they expect the sound field to be -- and then uses a singular real data point, aren't they really sustituting 'fake' (not necessarily invalid) effective data points for real ones?
The more data points the better which, as I recall, is kind of why we moved from mono to stereo back in the 1950's.

But please note that your ears have only two data points, yet you are able to hear a three dimensional sound field.  If two ears can do it, why can't two microphones?

Before reading -- note that there is a difference between 'HEARING' (includes the mental, head and ear characteristics) and 'SOUND' which is the pressure measurement thing.

Two microphones can do it just like two ears -- there is more information than just the simple math/physics of the sound field itself.  The brain can process directional hints like frequency response associated with outside ear/head shape, and also use mental imaging.

So, if you are talking about a computer without the brain power of the human/animal brain, then we are stuck with the the simple physics and a priori 'guesses'  (based upon expected environment.)

With all of the actual physics (without any mental imaging), plus mental imaging  available ot humans, there can be sythesized information that goes beyond the simple physics.  However, to be intellectually honest -- that information that the human brain can synthesize, the ability to use the shape/structure of the ears' environment and the hard-core physics of the environment -- that is GREATER than just the two sensors.  That is why more information can be gleaned.

So, one has to ask, are they talking about 'SOUND', or are they talking about 'HEARING'.  Hearing can gather more information (whether physically real or not), than just SOUND.

Those talking about 'imaging' beyond what can be gathered by math calculations based just on the two point sensors are really talking about HEARING -- not just SOUND.  This is probably where the confusion happens.

John

## Re: Help me understand why sound is one dimensional

##### Reply #59 – 2018-07-20 10:34:36
However, to be intellectually honest -- that information that the human brain can synthesize, the ability to use the shape/structure of the ears' environment and the hard-core physics of the environment -- that is GREATER than just the two sensors.  That is why more information can be gleaned.

Right. You could put it this way: There are a lot of assumptions built into human hearing. Some of them are learned, others are "wired in". This is a reason why hearing can be fooled and occasionally produces wrong impressions.

Stereo only works because of this. A phantom source isn't anything physical. There is no phantom source in the sound field. It is the post-processing of the signal from our two sensors (ears), which creates (the impression of) the phantom source.

You could say that with stereo, human hearing gets it consistently wrong. Stereo is a way of using a specific deficiency of human hearing to fool it into hearing a 3D sound field that isn't there. We all know that this illusion breaks down easily (sweet spot etc.).

## Re: Help me understand why sound is one dimensional

##### Reply #60 – 2018-07-20 12:31:22
However, to be intellectually honest -- that information that the human brain can synthesize, the ability to use the shape/structure of the ears' environment and the hard-core physics of the environment -- that is GREATER than just the two sensors.  That is why more information can be gleaned.

Right. You could put it this way: There are a lot of assumptions built into human hearing. Some of them are learned, others are "wired in". This is a reason why hearing can be fooled and occasionally produces wrong impressions.

Stereo only works because of this. A phantom source isn't anything physical. There is no phantom source in the sound field. It is the post-processing of the signal from our two sensors (ears), which creates (the impression of) the phantom source.

You could say that with stereo, human hearing gets it consistently wrong. Stereo is a way of using a specific deficiency of human hearing to fool it into hearing a 3D sound field that isn't there. We all know that this illusion breaks down easily (sweet spot etc.).
Good -- that is the kind of point that I was trying to make.  We all (including me) have this trouble of seperating real (simple) physics from what our minds can do.  Normally, to me, the real world is how I perceive it -- but that is actually not true.  The same kind of thing applies to audio perception.

All of this said - even though we have clarified the difference between HEARING and SOUND, for the purposes of audio ENJOYMENT, hearing is more of the goal than sound.  Sound (I mean, the physics and technology to reproduce) is important -- making a lot of hearing enjoyment possible, so we cannot discredit either.

Where we get in trouble is doing the reverse of 'Sound directly helping to make hearing work' -- which is valid.
Trying to describe the real world (reality) by depending solely on what one simply hears can cause confusion -- as you implied above, perceptual errors.

It is so very nice that English (and probably a lot of other languages) allow us to distinguish between SOUND (the physics) and HEARING (what our brains perceive.)  If we don't distinguish between the two, audiophile-land can be very confusing, and is probably a major reason for all of the 'audio-religion', and wine-tasting-esque descriptions of audio out there.  There are real technical descriptions available, but until the idea of SOUND and HEARING are seperated, then a lot of people are going to stay confused, but not know it.

John

## Re: Help me understand why sound is one dimensional

##### Reply #61 – 2018-07-20 16:03:28
If we don't distinguish between the two, audiophile-land can be very confusing, and is probably a major reason for all of the 'audio-religion', and wine-tasting-esque descriptions of audio out there.  There are real technical descriptions available, but until the idea of SOUND and HEARING are seperated, then a lot of people are going to stay confused, but not know it.

Quite. In my view, the inability (and unwillingness) to acknowledge the role of one's own brain in what they perceive, is among the most prominent reasons for their cluelessnes. It is getting fuelled by the pervasive style of gear reviews, where the item that is reviewed is being put into the active position. Anything that people allegedly hear is said to be the "work" of the item tested. In this manner, even benign pieces of kit like connectors have a "sonic signature", affect spatial perception in mysterious ways (i.e. put instruments in certain places), and such hogwash. It is basically a projection. Something that is a function of one's brain is projected onto a piece of kit.

In theory, if people were responsible and rational, they would judge their gear according to what it does to the signal, not what it does to the hearing. But it would require a level of technical sophistication in the audience that is just unrealistic.

## Re: Help me understand why sound is one dimensional

##### Reply #62 – 2018-07-20 21:33:56
IMHO the 1D point of view don't conceptualize the reality because all audio measurements are performed by people who have the sound field in mind.

If a person has a picture of what they expect the sound field to be -- and then uses a singular real data point, aren't they really sustituting 'fake' (not necessarily invalid) effective data points for real ones?  No matter what you are imagining, there has to be some kind of framework -- and in space, there are normally 3 dimensions.  One can abstractly create more dimensions for some kind of analysis purpose, but in reality there are three dimensions in space.   Adding more dimensions isn't just describing space, but rather some kind of hyperspace (no scifi here.)

John
We have a tension, an intensity and time at the input of the loudspeaker coil, we can also try to link the voltage and the intensity through an imaginary thing called phase... also linked with the coil motion... and the air motion... abstraction is infinitely complex.
I only matter about what i'm imagining when i perform a measurement, the loudspeaker surface is radiating within two modes, a pistonic and radiative motion that generate a complex soundfield composed of a cloud of air of physical elementary particles moving relatively coherentely with the emissive surfaces when you are close to them and doing unpredictible things when you get farther (everyting is also highly impacted by the signals)
You should also add all the reflexions and the air volume when you are in a room, as you are probably awared of expertise is everthing and a clever measurement can validate a very complex theory.
If we don't matter about how many dimensions to use, could you say if there is a way to beat a human brain in this field of competence ?

... i'm not as intelligent as Garry Kasparov, but deeper blue is still biting the dust.

## Re: Help me understand why sound is one dimensional

##### Reply #63 – 2018-07-21 00:39:12
IMHO the 1D point of view don't conceptualize the reality because all audio measurements are performed by people who have the sound field in mind.

If a person has a picture of what they expect the sound field to be -- and then uses a singular real data point, aren't they really sustituting 'fake' (not necessarily invalid) effective data points for real ones?  No matter what you are imagining, there has to be some kind of framework -- and in space, there are normally 3 dimensions.  One can abstractly create more dimensions for some kind of analysis purpose, but in reality there are three dimensions in space.   Adding more dimensions isn't just describing space, but rather some kind of hyperspace (no scifi here.)

John
We have a tension, an intensity and time at the input of the loudspeaker coil, we can also try to link the voltage and the intensity through an imaginary thing called phase... also linked with the coil motion... and the air motion... abstraction is infinitely complex.
I only matter about what i'm imagining when i perform a measurement, the loudspeaker surface is radiating within two modes, a pistonic and radiative motion that generate a complex soundfield composed of a cloud of air of physical elementary particles moving relatively coherentely with the emissive surfaces when you are close to them and doing unpredictible things when you get farther (everyting is also highly impacted by the signals)
You should also add all the reflexions and the air volume when you are in a room, as you are probably awared of expertise is everthing and a clever measurement can validate a very complex theory.
If we don't matter about how many dimensions to use, could you say if there is a way to beat a human brain in this field of competence ?

... i'm not as intelligent as Garry Kasparov, but deeper blue is still biting the dust.

All of the physical stuff being described can be modeled by a competent mechanical/electrical engineering team.  Modeled so accurately that a 'virtual' copy of the speaker can likely predict the behavior incredibly accurately (including the enviornment.)  All of the things like 'standing waves' on a speaker diaphragm are 'old hat', and can be predicted fairly well.

Where we do have troubles is modeling exactly what the human hearing system (incl internal/external ears, head, brain, etc) perceives.  We can predict the frequency resp/phase relasionships of what enters the ear, and even model some of the ear, but that is as far as it goes.  Beyond this level is where the 'audiophile' mode becomes much more valid.

For example, I cannot predict what you will hear, and how you will react to a given stimulus.  Will it seem 'pretty' to you or seem 'ugly'?  I don't know, and won't even attempt to scientificially predict.  (I can certainly guess, however :-)).

As an engineer, all I can claim is to be able to parametrically describe or create a design (either of my own creation or someone else.)  When in a field where I am competent (and it is NOT speakers), I can create a design that is almost as perfect as the situation (costs, parts availability, software tools, CPU capability) allows.  (I am both a full EE, DSP person and operating systems software designer -- all with at least 3 decades experience and successful.)  BUT, I'd suck at speaker or microphone design -- I know the general physics, but not the techniques, technology or have any experience.

So real engineers can do a lot, but cannot predict what people can really perceive.  I know my limitations, and happily admit them -- otherwise, cannot be credible.  I am an engineer, not a able to do a mind meld to really understand what people feel/think.

John

## Re: Help me understand why sound is one dimensional

##### Reply #64 – 2018-07-21 06:56:05
All of the physical stuff being described can be modeled by a competent mechanical/electrical engineering team.  Modeled so accurately that a 'virtual' copy of the speaker can likely predict the behavior incredibly accurately (including the enviornment.)  All of the things like 'standing waves' on a speaker diaphragm are 'old hat', and can be predicted fairly well.

It is perhaps time to add a new knowledge to your personal culture... it hadn't been done yet, i would be very pleased to see one of that kind of study before my death.
In an effort to stay in touch with the topic, i can say that the sound propagation in our environement (air, room and objects) is infinitely complex and unpredictible by nature, and the 1D point of view is a good explanation for the children but not for an adult.

## Re: Help me understand why sound is one dimensional

##### Reply #65 – 2018-07-21 12:37:26
All of the physical stuff being described can be modeled by a competent mechanical/electrical engineering team.  Modeled so accurately that a 'virtual' copy of the speaker can likely predict the behavior incredibly accurately (including the enviornment.)  All of the things like 'standing waves' on a speaker diaphragm are 'old hat', and can be predicted fairly well.

It is perhaps time to add a new knowledge to your personal culture... it hadn't been done yet, i would be very pleased to see one of that kind of study before my death.
In an effort to stay in touch with the topic, i can say that the sound propagation in our environement (air, room and objects) is infinitely complex and unpredictible by nature, and the 1D point of view is a good explanation for the children but not for an adult.

The environment can also be included in models.  But, at a certain point, it is silly to go into more detail.  There are so many kinds of environments, that a generally applicable design will work well.

This is all about the nonsensical 'audiophile' reasoning (and pseudo-wine tasting language) vs. the real state of engineering and research.  There are still alot of snake oil salesemen selling inferior product with 'personality' vs. very accurate equipment.
I vote on the side of real, accurate engineering vs. the overly expensive snake oil.  Too many people without real engineering backgrounds get taken in by snake oil marketing.

In some cases, some of the snake oil marketing IS backed by sound engineering, but that is really kind of sad.  People are being dys-educated into being idiots in the guise of pseudo-tech.

Real world engineering thinking and work is where the real advances are made (or, in the case of a lot of legacy technologies -- e.g. most audio stuff), already have been made.  Please refer to the rather curious love of vacuum tubes (definitely legacy, but cute technology.)  It is damned hard to get really good distortion and bandwidth on tube gear, but they try (barely succeeding) -- and some make money at it, esp with the snake oil behind it.  (I started designing with 'tubes' years ago -- I know what I am talking about.)

My guess is that because audio (in almost all ways) has advanced almost as far as it can -- some of the marketeers who take advantage of the non-engineering-knowing people and instead look backwards.  Sure -- 'adequate' quality can be had with 'tubes', but why do it?   Marketeering (coined word -- marketing based upon feeling instead of fact, with a bit of hogwash added in), knowing that selling goods based upon technical advantage is now nearly specious (given competent, up-to-date design.)

John

## Re: Help me understand why sound is one dimensional

##### Reply #66 – 2018-07-21 13:26:42
The environment can also be included in models.  But, at a certain point, it is silly to go into more detail.  There are so many kinds of environments, that a generally applicable design will work well.
All good measuring softwares that i've tested are unable to corellate the measurements and the theory, the calculated room modes are always wrong.
The devil is in the details, and the lack of these details is killing the math models accuracy.

This is all about the nonsensical 'audiophile' reasoning (and pseudo-wine tasting language) vs. the real state of engineering and research.  There are still alot of snake oil salesemen selling inferior product with 'personality' vs. very accurate equipment.
I vote on the side of real, accurate engineering vs. the overly expensive snake oil.  Too many people without real engineering backgrounds get taken in by snake oil marketing.
In some cases, some of the snake oil marketing IS backed by sound engineering, but that is really kind of sad.  People are being dys-educated into being idiots in the guise of pseudo-tech.
Real world engineering thinking and work is where the real advances are made (or, in the case of a lot of legacy technologies -- e.g. most audio stuff), already have been made.  Please refer to the rather curious love of vacuum tubes (definitely legacy, but cute technology.)  It is damned hard to get really good distortion and bandwidth on tube gear, but they try (barely succeeding) -- and some make money at it, esp with the snake oil behind it.  (I started designing with 'tubes' years ago -- I know what I am talking about.)
My guess is that because audio (in almost all ways) has advanced almost as far as it can -- some of the marketeers who take advantage of the non-engineering-knowing people and instead look backwards.  Sure -- 'adequate' quality can be had with 'tubes', but why do it?   Markettering (coined word -- marketing based upon feeling instead of fact), knowing that selling goods based upon technical advantage is now nearly specious (given competent, up-to-date design.)
John
The only way to go is to calculate and measure by yourself IMHO, the market is saturated of junk product and the good ones are also junk when used inappropriately.

## Re: Help me understand why sound is one dimensional

##### Reply #67 – 2018-07-21 14:01:29
The environment can also be included in models.  But, at a certain point, it is silly to go into more detail.  There are so many kinds of environments, that a generally applicable design will work well.
All good measuring softwares that i've tested are unable to corellate the measurements and the theory, the calculated room modes are always wrong.
The devil is in the details, and the lack of these details is killing the math models accuracy.

This is all about the nonsensical 'audiophile' reasoning (and pseudo-wine tasting language) vs. the real state of engineering and research.  There are still alot of snake oil salesemen selling inferior product with 'personality' vs. very accurate equipment.
I vote on the side of real, accurate engineering vs. the overly expensive snake oil.  Too many people without real engineering backgrounds get taken in by snake oil marketing.
In some cases, some of the snake oil marketing IS backed by sound engineering, but that is really kind of sad.  People are being dys-educated into being idiots in the guise of pseudo-tech.
Real world engineering thinking and work is where the real advances are made (or, in the case of a lot of legacy technologies -- e.g. most audio stuff), already have been made.  Please refer to the rather curious love of vacuum tubes (definitely legacy, but cute technology.)  It is damned hard to get really good distortion and bandwidth on tube gear, but they try (barely succeeding) -- and some make money at it, esp with the snake oil behind it.  (I started designing with 'tubes' years ago -- I know what I am talking about.)
My guess is that because audio (in almost all ways) has advanced almost as far as it can -- some of the marketeers who take advantage of the non-engineering-knowing people and instead look backwards.  Sure -- 'adequate' quality can be had with 'tubes', but why do it?   Markettering (coined word -- marketing based upon feeling instead of fact), knowing that selling goods based upon technical advantage is now nearly specious (given competent, up-to-date design.)
John
The only way to go is to calculate and measure by yourself IMHO, the market is saturated of junk product and the good ones are also junk when used inappropriately.

When it comes down to it, I agree with you.  It is probably impossible for even an experienced engineer to be able to 100% a-priori detect real vs. exaggerated.  (I won't claim that all of the excessive claims are made about bad equipment -- just exaggerated.  Not all wonderful claims are exaggerations either.)

So, IMO - you are 100% correct -- paraphrasing your main point:  listen for oneself.  Decide for oneself.

John

## Re: Help me understand why sound is one dimensional

##### Reply #68 – 2018-07-24 11:27:47
Thanks for not making me feel quite so silly. My friend is a maths professor, and I believe his assertion. I just don't understand how you can have that type of information in a single dimension (time).
Perhaps you can get him to clarify.

Well. I tried. But as I initially started out with, its quite complicated. But again, happy to see that that there are other people here who are confused. And also, other people who seem to know what they are talking about, and explains it in a way that makes sense. I am in the strange position to where I am certain he is correct, without initially knowing why. I guess his knowledge in the field of mathematics (and my lack of understanding) creates a situation to where it was hard convey and understand the explanation. Everyone involved here has certainly contributed to both my understanding as well as my initial confusion.

## Re: Help me understand why sound is one dimensional

##### Reply #69 – 2018-07-24 15:18:23
You could very well ask him for something to be copied/pasted here. It would surprise me if there is not enough of the (relevant) math skills here to catch and explain (or posstibly rectify) the main point.
High Voltage socket-nose-avatar

## Re: Help me understand why sound is one dimensional

##### Reply #70 – 2018-07-24 18:02:19
clever mustache man mentions the one dimension denomination around 2mn of the video for those who "ain't got no time for that". maybe that helps a little? if only thanks to an appeal to MIT's authority^_^.

## Re: Help me understand why sound is one dimensional

##### Reply #71 – 2018-07-24 22:09:04
The function y=f(x) is one dimensional. A two dimensional function would have the form y=f(x1,x2).

Why not y=f(x,t) ?

Related http://www.feynmanlectures.caltech.edu/I_47.html

edit: I guess I'am struggling between basic physics prototype and math representation of it. And somewhere along the path the word 'sound' seems to loose any meaning.
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## Re: Help me understand why sound is one dimensional

##### Reply #72 – 2018-07-24 23:33:24
The function y=f(x) is one dimensional. A two dimensional function would have the form y=f(x1,x2).

Why not y=f(x,t) ?

Related http://www.feynmanlectures.caltech.edu/I_47.html
Strictly, the f(x,t) is indeed two dimensional -- 'f' is a function of two variables, where time is one of them.  In this case, there is nothing magical about time.  Just as (for example), the sin function in sin(a*t) is also a function whose value is a function of time.

John

## Re: Help me understand why sound is one dimensional

##### Reply #73 – 2018-07-25 00:46:37
I'd like to point out that I think much of the confusion here is regarding the usage of the word "dimension". The graph of a one-variable function y = f(x) is indeed two-dimensional (that is, you need two dimensions to draw the function) even if you only have one independent variable x.

To the OP; you say in your first message, "I would assume sound also has at least two axis, one representing time" -- that is absolutely correct, sound is a wave that propagates through space and time, so you need at least one spatial independent variable and the time independent variable; a third variable also exists here, the pressure, which is the dependent variable, which, when the wave equation is solved, gives the pressure as a function of time and space.

Then you say, "My friend makes the claim that there only is one". Could it be possible your friend is thinking of the typical expansion-compression cycle, like that of a Slinky, which goes back and forth in one spatial dimension but otherwise also advances in time?

As others here have pointed out, it'd be useful to see, verbatim, what your friend says, from which we can attempt to deduce what was meant, and if needed, correct what they said.
Lossless: flac --best --verify
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## Re: Help me understand why sound is one dimensional

##### Reply #74 – 2018-07-25 01:46:09
I'd like to point out that I think much of the confusion here is regarding the usage of the word "dimension". The graph of a one-variable function y = f(x) is indeed two-dimensional (that is, you need two dimensions to draw the function) even if you only have one independent variable x.

To the OP; you say in your first message, "I would assume sound also has at least two axis, one representing time" -- that is absolutely correct, sound is a wave that propagates through space and time, so you need at least one spatial independent variable and the time independent variable; a third variable also exists here, the pressure, which is the dependent variable, which, when the wave equation is solved, gives the pressure as a function of time and space.

Then you say, "My friend makes the claim that there only is one". Could it be possible your friend is thinking of the typical expansion-compression cycle, like that of a Slinky, which goes back and forth in one spatial dimension but otherwise also advances in time?

As others here have pointed out, it'd be useful to see, verbatim, what your friend says, from which we can attempt to deduce what was meant, and if needed, correct what they said.

This is starting to be a 'how many angels on the head of a pin' or a terminology discussion.  One can look at these things from too many directions (or dimensions. :-)).   Describing a function in the terms of dimensions is confusing because (as previous poster said), it all depends on the context -- so I wouldn't normally even use the term dimension in this context.   In a way, describing a function as having dimensions doens't really make much sense because it is a fuzzy meaning (dimensions regarding what?)   Some inputs to the function might not even be continuous - so how is that described to be a dimension in a common sense way?

One can say that space has so many dimensions (plus time), but a function having dimensions depends on what is being talked about -- almost ending up being a meaningless term without LOTS of qualification.

There is probably a pure math definition, and that is probably what should be used -- but it is still confusing (and I use LOTS of complicated functions all of the time!!!)

John