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Re: Help me understand why sound is one dimensional

Reply #75
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

I agree, using "dimension" for a function itself is confusing, which is why I clarified that usually one speaks of geometrical dimensions, in which the dimensions of the graph of a function does make sense.

But yes, until a more verbatim statement from the OP's friend comes, it's probably best to withhold judgement.
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Re: Help me understand why sound is one dimensional

Reply #76
I agree, using "dimension" for a function itself is confusing, which is why I clarified that usually one speaks of geometrical dimensions, in which the dimensions of the graph of a function does make sense.

But yes, until a more verbatim statement from the OP's friend comes, it's probably best to withhold judgement.

The way I understand it, the OP's friend must have referred to time as the one dimension. I can't believe that he wanted to restrict sound to one dimension in space - that would have been sound in a tube, for example.

Regarding sound as one-dimensional makes sense if you look at the sound in one particular location in space, for example the position of a microphone, or an ear. Seen this way, sound is a pressure that varies with time, i.e. a function of time that yields pressure. A one- dimensional function in the mathematical sense. After the microphone, the signal is electrical, but still it is a function of time, i.e. a one-dimensional function of time that yields voltage. In general, once you are in the electronics domain, sound is one-dimensional, since it is an electrical signal that varies with time. (More precisely, the electrical signal is only a representation of sound, not sound itself, but that's splitting hairs).

Note that we can't speak of a wave in this context. A wave is something that propagates through space (in one, two or 3 dimensions). Something that depends only on time doesn't propagate, hence can't be a wave. It can be a sample of a wave at some point in space.

The OP's friend probably wanted to highlight this fundamental difference: There is a soundfield in space, a 3D pressure wave, which is actually a four-dimensional phenomenon because it also varies with time. And there is an electronic representation of sound, which is what all our gear (including our ear) deals with, which is merely one or several electrical signals that vary with time.

This goes to show that recording sound is always a very "lossy" activity. You can't capture a soundfield as a whole, you can only capture it at certain locations where you can place a microphone. If you wanted to capture the entire soundfield, you could place microphones in a 3D grid throughout the space the soundfield occupies. But in order to cover the frequencies humans can perceive, the spacing of the microphones in the grid would have to be less than an inch, which makes the endeavor extremely impractical.

Re: Help me understand why sound is one dimensional

Reply #77
@pelmazo: All of that is quite possible, and I agree that once in the electronics domain, the "one-dimensional" nomenclature makes more sense. For me, without any context, the word "sound" implies the physical phenomenon of, as you very neatly elucidated, a pressure wave propagating through space and time, which can't be, thus, one-dimensional. This means that the OP's friend is probably talking about something else, quite possibly the signal that is captured by microphones or other devices, as you stated.

Alas, without further clarification from the OP and their friend, I'm not sure we'll get anywhere.
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Re: Help me understand why sound is one dimensional

Reply #78
Hold on now.

This is an oversimplification, but lets assume the waveform, which is one-dimensional, is sent through a static signal chain, eventually moving a set of voicecoils in a static environment (in other words, nothing else but the waveform is time-dependent) then the pressure of the medium at any given point in three dimensional space is dependent only on the waveform and is thus also only one-dimensional.
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Re: Help me understand why sound is one dimensional

Reply #79
This is an oversimplification, but lets assume the waveform, which is one-dimensional, is sent through a static signal chain, eventually moving a set of voicecoils in a static environment (in other words, nothing else but the waveform is time-dependent) then the pressure of the medium at any given point in three dimensional space is dependent only on the waveform and is thus also only one-dimensional.

You can make every 4-dimensional function one-dimensional by fixing 3 of the free variables. If you fix all spatial variables, leaving only the time free, then you have a one-dimensional function that describes the pressure over time at this fixed point in space. Of course, you can do this for any given point, as you say.

Just for the hell of it, you could instead fix two spatial dimensions and time, and keep the remaining spatial dimension free. You would get, for example, a function that describes pressure along a line parallel to the X axis, for a certain point in time, where the position of the line, i.e. its Y and Z position, is fixed. Picture a stroboscope flash illuminating a vibrating string.

This is a theoretical view, for sure, but I hope the point is clear: A 4-dimensional function can be converted to an "array" of lesser-dimensional functions, one for each combination of the variables that have been eliminated. This doesn't change the fundamental situation.

Re: Help me understand why sound is one dimensional

Reply #80
@pelmazo: All of that is quite possible, and I agree that once in the electronics domain, the "one-dimensional" nomenclature makes more sense. For me, without any context, the word "sound" implies the physical phenomenon of, as you very neatly elucidated, a pressure wave propagating through space and time, which can't be, thus, one-dimensional.

The dimensionality of a sound wave depends on the boundary conditions.  1, 2 or 3D are all possible.  Stringed instruments are an obvious example of 1 D propagation.  No way to have more than 1D when your waveform is confined to a (subwavelength diameter) line. 

Re: Help me understand why sound is one dimensional

Reply #81
...and as I said earlier, and although it doesn't matter, for those who think this is about geometry with time being a fourth dimension, the magneto force pushes the voice coil of a driver in a straight line.
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Re: Help me understand why sound is one dimensional

Reply #82
You can make every 4-dimensional function one-dimensional by fixing 3 of the free variables. If you fix all spatial variables, leaving only the time free, then you have a one-dimensional function that describes the pressure over time at this fixed point in space. Of course, you can do this for any given point, as you say.

[...]

This is a theoretical view, for sure, but I hope the point is clear: A 4-dimensional function can be converted to an "array" of lesser-dimensional functions, one for each combination of the variables that have been eliminated. This doesn't change the fundamental situation.
Hopefully the point is clear since it seemed to me that the straw vote was that sound was multidimensional.  Heck, I also made the comment in error that an anechoic environment increases the dimension count.

The next question is the dimensionality of how hard-headed the participants are in this discussion.
Is 24-bit/192kHz good enough for your lo-fi vinyl, or do you need 32/384?

Re: Help me understand why sound is one dimensional

Reply #83
@pelmazo: All of that is quite possible, and I agree that once in the electronics domain, the "one-dimensional" nomenclature makes more sense. For me, without any context, the word "sound" implies the physical phenomenon of, as you very neatly elucidated, a pressure wave propagating through space and time, which can't be, thus, one-dimensional.

The dimensionality of a sound wave depends on the boundary conditions.  1, 2 or 3D are all possible.  Stringed instruments are an obvious example of 1 D propagation.  No way to have more than 1D when your waveform is confined to a (subwavelength diameter) line. 

This depends highly on what is meant with "dimension"; if it's the count of independent variables, since you always have at least one spatial dimension, and the time dimension, the minimum would be two-dimensional. Now, if you mean how the wave is "confined", that's different altogether.
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Re: Help me understand why sound is one dimensional

Reply #84
It is a ginormous understatement that my linear algebra is rusty, but have a lood at the original post:

I try to understand my friends argument that sound, and thus music, is one dimensional. An image consists of a matrix of numbers placed on two axis. In my limited understanding, I would assume sound also has at least two axis, one representing time. My friend makes the claim that there only is one. I tried googling this to no avail. Anyone up for the task?

PS: Ignore the post before this edit at 25 after the hour.
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Re: Help me understand why sound is one dimensional

Reply #85
Yeah, I'm really hoping for sizetwo to show up and tell us if they've spoken to their mathematician friend; I really would like to know what it's all about.
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Re: Help me understand why sound is one dimensional

Reply #86
@pelmazo: All of that is quite possible, and I agree that once in the electronics domain, the "one-dimensional" nomenclature makes more sense. For me, without any context, the word "sound" implies the physical phenomenon of, as you very neatly elucidated, a pressure wave propagating through space and time, which can't be, thus, one-dimensional.

The dimensionality of a sound wave depends on the boundary conditions.  1, 2 or 3D are all possible.  Stringed instruments are an obvious example of 1 D propagation.  No way to have more than 1D when your waveform is confined to a (subwavelength diameter) line. 

This depends highly on what is meant with "dimension"; if it's the count of independent variables, since you always have at least one spatial dimension, and the time dimension,

You can sound without a time dimension. Standing waves for instance.  All comes down to your boundary conditions. 

Re: Help me understand why sound is one dimensional

Reply #87
@pelmazo: All of that is quite possible, and I agree that once in the electronics domain, the "one-dimensional" nomenclature makes more sense. For me, without any context, the word "sound" implies the physical phenomenon of, as you very neatly elucidated, a pressure wave propagating through space and time, which can't be, thus, one-dimensional.

The dimensionality of a sound wave depends on the boundary conditions.  1, 2 or 3D are all possible.  Stringed instruments are an obvious example of 1 D propagation.  No way to have more than 1D when your waveform is confined to a (subwavelength diameter) line. 

This depends highly on what is meant with "dimension"; if it's the count of independent variables, since you always have at least one spatial dimension, and the time dimension,

You can sound without a time dimension. Standing waves for instance.  All comes down to your boundary conditions. 

That's not true. As its name indicates, a standing wave oscillates in time but has a stationary, or standing, spatial dependence; at any chosen point along the wave, the amplitude is constant and depends solely on the location of the chosen point, such that the equation of the resultant wave looks like this.

All of this is a consequence of the wave equation (of which the acoustic wave equation, the equation that describes the physics of sound, is a specific case) being a partial differential equation in time and at least one spatial variable, so it's only natural for time to show up in the solutions as an explicit independent variable.

But I feel we digress; until the OP clarifies the situation, I feel we'll only go around in circles, quibbling over minutiae and semantics.
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Re: Help me understand why sound is one dimensional

Reply #88
Not an area of particular expertise for me, but doesn't a sound wave propagate and aren't all of spatial dimensional properties then determined by the interaction with the propagation media and not the wave itself?

Re: Help me understand why sound is one dimensional

Reply #89
Thinking further - with an image there can be multiple points for y for a given value of x, so you need to express it as a matrix (a 2 dimensional array) of values for every (x,y) point.

With sound there is only a single point relative to a given axis and thus you only need a one dimensional array.

Re: Help me understand why sound is one dimensional

Reply #90
@pelmazo: All of that is quite possible, and I agree that once in the electronics domain, the "one-dimensional" nomenclature makes more sense. For me, without any context, the word "sound" implies the physical phenomenon of, as you very neatly elucidated, a pressure wave propagating through space and time, which can't be, thus, one-dimensional.

The dimensionality of a sound wave depends on the boundary conditions.  1, 2 or 3D are all possible.  Stringed instruments are an obvious example of 1 D propagation.  No way to have more than 1D when your waveform is confined to a (subwavelength diameter) line. 

This depends highly on what is meant with "dimension"; if it's the count of independent variables, since you always have at least one spatial dimension, and the time dimension,

You can sound without a time dimension. Standing waves for instance.  All comes down to your boundary conditions. 

That's not true. As its name indicates, a standing wave oscillates in time but has a stationary, or standing, spatial dependence; at any chosen point along the wave, the amplitude is constant and depends solely on the location of the chosen point, such that the equation of the resultant wave looks

If amplitude is solely a function of position than it is not a function of time.  A standing wave with 1 spatial dimension is therefore a 1D waveform. 

Re: Help me understand why sound is one dimensional

Reply #91
That's not true. As its name indicates, a standing wave oscillates in time but has a stationary, or standing, spatial dependence; at any chosen point along the wave, the amplitude is constant and depends solely on the location of the chosen point, such that the equation of the resultant wave looks like this.
Can i answer a question ?
A real standing wave is permanently consuming its own energy in the air, so its amplitude should always be different no ?

Re: Help me understand why sound is one dimensional

Reply #92
@pelmazo: All of that is quite possible, and I agree that once in the electronics domain, the "one-dimensional" nomenclature makes more sense. For me, without any context, the word "sound" implies the physical phenomenon of, as you very neatly elucidated, a pressure wave propagating through space and time, which can't be, thus, one-dimensional.

The dimensionality of a sound wave depends on the boundary conditions.  1, 2 or 3D are all possible.  Stringed instruments are an obvious example of 1 D propagation.  No way to have more than 1D when your waveform is confined to a (subwavelength diameter) line. 

This depends highly on what is meant with "dimension"; if it's the count of independent variables, since you always have at least one spatial dimension, and the time dimension,

You can sound without a time dimension. Standing waves for instance.  All comes down to your boundary conditions. 

That's not true. As its name indicates, a standing wave oscillates in time but has a stationary, or standing, spatial dependence; at any chosen point along the wave, the amplitude is constant and depends solely on the location of the chosen point, such that the equation of the resultant wave looks

If amplitude is solely a function of position than it is not a function of time.  A standing wave with 1 spatial dimension is therefore a 1D waveform. 


I suppose that's fair enough.

That's not true. As its name indicates, a standing wave oscillates in time but has a stationary, or standing, spatial dependence; at any chosen point along the wave, the amplitude is constant and depends solely on the location of the chosen point, such that the equation of the resultant wave looks like this.
Can i answer a question ?
A real standing wave is permanently consuming its own energy in the air, so its amplitude should always be different no ?

If you mean that friction/drag due to the air will make the wave eventually die out, that's true, but you'll see that textbook derivations of these equations usually neglect these effects of attenuation.
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Re: Help me understand why sound is one dimensional

Reply #93
If you mean that friction/drag due to the air will make the wave eventually die out, that's true, but you'll see that textbook derivations of these equations usually neglect these effects of attenuation.

A pseudo periodic function will give the real life taste to the equation.

Re: Help me understand why sound is one dimensional

Reply #94
If amplitude is solely a function of position than it is not a function of time.  A standing wave with 1 spatial dimension is therefore a 1D waveform.

It's still two dimensions: position and amplitude (and amplitude requires a second axis or dimension to distinguish, so there's your 2D).  Otherwise your wave could have amplitude 0, 1, or whatever and still be considered the "same" wave - and I think your ears would clearly tell you they're not. 

Re: Help me understand why sound is one dimensional

Reply #95
You're mixing up all kinds of things: spatial dimensions, spatial and temporal dimensions, dimensions of waveform visualizations, "dimensions of functions" (which doesn't exist) ...

Sound, defined as a mechanical wave, propagates through 3D space over time.

You can cut down spatial dimensions until you have a fixed position where you just measure pressure (an amplitude) over time. This is also what you get when you quantize it. (Even if the time axis is implicit, it's still there.)

That's it.
"I hear it when I see it."

Re: Help me understand why sound is one dimensional

Reply #96
If amplitude is solely a function of position than it is not a function of time.  A standing wave with 1 spatial dimension is therefore a 1D waveform.

It's still two dimensions: position and amplitude (and amplitude requires a second axis or dimension to distinguish, so there's your 2D).  Otherwise your wave could have amplitude 0, 1, or whatever and still be considered the "same" wave - and I think your ears would clearly tell you they're not. 
Incorrect.

You seem to be unable to understand the difference between projection of a function, and mapping of values. We've tried to explain this to exhaustion, but it seems we're running against a brick wall.

Re: Help me understand why sound is one dimensional

Reply #97
It could be consided one dimensional given that our eardrums have a single axis.
In the beginning there was ONLY noise, then came the signal.

 
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