Re: Help me understand why sound is one dimensional
Reply #75 – 2018-07-25 02:11:15

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.