3dimensional wave propogation.

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In summary, the conversation discusses the function that represents a 3 dimensional sine wave and the different contexts in which it can be applied. The function is described as a sine wave with the z-axis on the circumference of a circle, with examples given for both axisymmetric and radially symmetric waves. The question remains open-ended, with the speakers expressing their interest in the topic and discussing various solutions and approaches for studying waves.
  • #1
Bradyns
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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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  • #2
Bradyns said:
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...
 
  • #3
Essentially, the function for this:
sinani2.gif


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))
 
  • #4
Bradyns said:
Essentially, the function for this:
sinani2.gif


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.
 
  • #5
berkeman said:
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. ^_^
 
  • #6
Just solve the wave equation in three dimensions, if you are only interested in isotropic propogation then set all the angular derivatives to zero.
 
  • #7
HomogenousCow said:
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]
 
  • #8
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.
 

1. What is 3-dimensional wave propagation?

3-dimensional wave propagation is the study of how waves, such as light, sound, or electromagnetic waves, travel and interact in three-dimensional space. This includes understanding how waves behave and change as they move through different mediums and encounter obstacles or boundaries.

2. How is 3-dimensional wave propagation different from 2-dimensional wave propagation?

In 3-dimensional wave propagation, waves travel and interact in three dimensions, whereas in 2-dimensional wave propagation, waves only travel and interact in two dimensions. This means that in 3-dimensional wave propagation, there are more variables to consider, such as the direction of propagation, polarization, and diffraction, which can have a significant impact on the behavior of the wave.

3. What are some real-world applications of 3-dimensional wave propagation?

3-dimensional wave propagation has many practical applications, such as in wireless communication, medical imaging, and sonar technology. It is also crucial in understanding and predicting natural phenomena, such as earthquakes and weather patterns.

4. How is 3-dimensional wave propagation studied and measured?

Scientists use a variety of techniques to study and measure 3-dimensional wave propagation, including computer simulations, mathematical models, and experiments using specialized equipment, such as oscilloscopes and spectrometers.

5. What are some challenges in studying 3-dimensional wave propagation?

One of the main challenges in studying 3-dimensional wave propagation is the complexity of the mathematical equations and models used to describe and predict wave behavior. Additionally, factors such as interference, diffraction, and scattering can make it challenging to accurately measure and analyze wave propagation in real-world situations.

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