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3dimensional wave propogation.

by Bradyns
Tags: function, sine, trig, wave
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Bradyns
#1
Feb19-13, 04:57 PM
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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berkeman
#2
Feb19-13, 05:13 PM
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Quote Quote by Bradyns View Post
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
#3
Feb19-13, 05:27 PM
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))

berkeman
#4
Feb19-13, 05:28 PM
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3dimensional wave propogation.

Quote Quote by Bradyns View Post
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([itex]\sqrt{x^{2}+y^{2}}[/itex])
Oh, I misunderstood your question then. I thought you wanted it to be symmetric in 3 dimensions, not just 2.
Bradyns
#5
Feb19-13, 05:30 PM
P: 20
Quote Quote by berkeman View Post
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
#6
Feb20-13, 01:51 AM
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.
jasonRF
#7
Feb27-13, 06:49 PM
P: 698
Quote Quote by HomogenousCow View Post
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:
[tex]
f(x,y,z,t) = \sin\left(k_x x + k_y y + k_z z - \omega t \right)
[/tex]
olivermsun
#8
Feb27-13, 08:59 PM
P: 852
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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