Quote from: blurry_light on 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.

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.

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.

@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.

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.

Quote from: blurry_light on 2018-07-26 13:16:16

@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. 

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?

Quote from: saratoga on 2018-07-26 19:20:31

Quote from: blurry_light on 2018-07-26 13:16:16

@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,

Quote from: blurry_light on 2018-07-26 20:09:38

Quote from: saratoga on 2018-07-26 19:20:31

Quote from: blurry_light on 2018-07-26 13:16:16

@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. 

Quote from: saratoga on 2018-07-27 01:38:25

Quote from: blurry_light on 2018-07-26 20:09:38

Quote from: saratoga on 2018-07-26 19:20:31

Quote from: blurry_light on 2018-07-26 13:16:16

@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

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.

Quote from: blurry_light on 2018-07-27 02:43:03

Quote from: saratoga on 2018-07-27 01:38:25

Quote from: blurry_light on 2018-07-26 20:09:38

Quote from: saratoga on 2018-07-26 19:20:31

Quote from: blurry_light on 2018-07-26 13:16:16

@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. 

Quote from: blurry_light on 2018-07-27 02:43:03

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.

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.

Quote from: saratoga on 2018-07-27 20:14:02

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.