3dimensional wave propogation.

[Bradyns]

I thought the maths area would be the best place to ask..

What kind of function would represent a 3 dimensional sine wave?
A sine wave, where the z-axis lays on the circumference of a circle.

 

[berkeman]

I thought the maths area would be the best place to ask..

What kind of function would represent a 3 dimensional sine wave?
A sine wave, where the z-axis lays on the circumference of a circle.

What is the context of the question? The equation for a symmetric longitudinal wave in 3-D is straightforward, I think. But I'm not sure there is a solution for symmetric transverse waves in 3-D...

 

[Bradyns]

Essentially, the function for this:

There isn't really a context, I'm not currently studying anything relating to this, it just interests me to see the behaviour of waves.

I seem to have found it, by looking for an example image.
z = sinx(√(x²+y²))

 

[berkeman]

Essentially, the function for this:

There isn't really a context, I'm not currently studying anything relating to this, it just interests me to see the behaviour of waves.

I seem to have found it, by looking for an example image.
z = sin(\sqrt{x^{2}+y^{2}})

Oh, I misunderstood your question then. I thought you wanted it to be symmetric in 3 dimensions, not just 2.

 

[Bradyns]

Oh, I misunderstood your question then. I thought you wanted it to be symmetric in 3 dimensions, not just 2.

Actually, that would be interesting..

Thank you for the assistance though. ^_^

 

[HomogenousCow]

Just solve the wave equation in three dimensions, if you are only interested in isotropic propagation then set all the angular derivatives to zero.

 

[jasonRF]

Just solve the wave equation in three dimensions, if you are only interested in isotropic propagation then set all the angular derivatives to zero.

I think like others I am not certain what the OP really meant, but I interpreted the question this way too - perhaps because I have a general interest in waves. Anyway, an example of a 3D plane wave would be:
<br /> f(x,y,z,t) = \sin\left(k_x x + k_y y + k_z z - \omega t \right)<br />

 

[olivermsun]

The axisymmetric 2d wave is of interest in surface wave propagation from a point source. There you examine sin (kr-ωt) where r= sqrt(x^2 + y^2).

The radially symmetric 3d wave arises for acoustic (pressure) waves emanating from a point source. The relevant plane wave has the form sin (kr - ωt) for r = sort(x^2 + y^2 + z^2) as jasonRF states above.