# 3dimensional wave propogation.

Tags: function, sine, trig, wave
 P: 20 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.
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P: 41,258
 Quote by 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.
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...
 P: 20 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))
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3dimensional wave propogation.

 Quote by 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 = 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.
P: 20
 Quote by berkeman 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. ^_^
 P: 366 Just solve the wave equation in three dimensions, if you are only interested in isotropic propogation then set all the angular derivatives to zero.
P: 697
 Quote by HomogenousCow Just solve the wave equation in three dimensions, if you are only interested in isotropic propogation 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:
$$f(x,y,z,t) = \sin\left(k_x x + k_y y + k_z z - \omega t \right)$$
 P: 840 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.

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