Talk:Acoustic wave equation

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Number of dimensions[edit]

I am confused. How can you have a wave equation in N dimensions for N > 3 ? The Acoustic Wave Equation is supposed to represent a pressure wave propogating through space and time. Neglecting for a moment that String Theory allows for 10 or 11 dimensions, shouldn't a pressure wave exist in only three dimensions of space and one dimension of time? Rdrosson 04:08, 15 September 2005 (UTC)[reply]

It's merely a suggestion to make the article more concise by presenting the formula for the three dimensions at once (hence, N = 1, 2 and 3). Maybe consider to include the 1-dimensional discussion under the heading "Quantum Approach" (i.e. sound as infinitisemal displacement of air packets). Regards. Witger 08:05, 15 September 2005 (UTC)[reply]

The reason for presenting the 1D and 3D cases separately is that for most people, it is much easier to think in terms of 1D, especially when first learning new ideas. Moreover, you can learn most if not all of the essential concepts and fundamental principles in the 1D simplification without resorting to the more general, but also more difficult, 3D case. But, of course, we do live in a 3D world, and so once you learn the basics using the 1D equation, it is not all that difficult to move to the 3D equation, especially if you are comfortable with vectors, matrices, multivariable functions, vector calculus, etc. Rdrosson 12:31, 15 September 2005 (UTC)[reply]

c[edit]

The "c" symbol at the start of the first derivation is described as the speed of sound. At the end of the derivation, c is given a different meaning. When did the meaning change?Philius99 (talk) 12:02, 3 June 2009 (UTC)[reply]

If you are referring to

c={\sqrt {\frac {B}{\rho _{0}}}}

.

then it's still the speed of sound - and this is its dependence on the adiabatic bulk modulus

B

and ambient density

\rho _{0}

of the air/gas. If this was the c that caused confusion, then it might be worth appending is the speed of propagation to that line.--catslash (talk) 13:31, 3 June 2009 (UTC)[reply]

Density function[edit]

I'm looking for a set of equations that describe, instantaneously for a particular point a) it's change in density b) it's change in direction as a functions of it's reaction to an acoustic wave. I've seen some versions of the Navier-Stokes equations that do this, but for fluids in general, not air.

Would it be a good idea to link to them/expand on the subtleties with relevance to acoustics on this page?Philius99 (talk) 12:02, 3 June 2009 (UTC)[reply]