How does a 3D sine wave appear on a graph?

In summary, the conversation discusses the appearance of a three-dimensional sine wave and its possible variations depending on the addition of a third axis. The participants also mention the use of graphic calculators to generate different 3D graphs of sine waves. Overall, there is no one definitive representation of a 3D sine wave and it can be interpreted in various ways.
  • #1
SeManTics
13
0
What does a three-dimensional sine wave look like?

-Sam
 
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  • #3
Sine is a function of one variable, what higher dimensional analogue did you mean?
 
  • #4
It's just that I've seen too many three-dimensional crests representing electromagnetic waves, and I wanted to find out if the same was true for sine waves, or if sine waves are spiral-shaped, three-dimensionally.
 
  • #5
Remember: sine waves can be calculated using two axes (x and y) but what happens if we add a third axis of depth (z)? It would be interesting if in 3D form it looked more like a spiral than a wave.
Same with phi. We always look at it three-dimensionally, but what if we added depth...would it not be spiral-shaped, much like I'm supposing a sine wave is?
Remember: out of an infinite possible viewpoints, from only one will a three-dimensional object apear two-dimensional, and a two-dimensional object one-dimensional. We humans have that uniqueness in our perspectives.
 
  • #6
You may continue it in many ways, there is not one that is "the" 3-d sinewaveindeed I'd say that none of them is even "a" 3-d sinewave: it could look like ripples on a pond from a dropped stone (concentric), or ridges like a piece of corrugated cardboard.
 
  • #7
Get a graphic calculator that can do 3d graphs and put in something like:
Z = sin(x)*sin(y)
or
Z = Sin(xy)
or
Z = sin(x) + sin(y)

etc etc...
 

1. What is a 3D sine wave?

A 3D sine wave is a three-dimensional representation of a sinusoidal function, which is a mathematical curve that oscillates up and down in a smooth, repeating pattern. In a 3D sine wave, the amplitude (height) and frequency (spacing between peaks) of the sine wave can be visualized in three dimensions.

2. How is a 3D sine wave created?

A 3D sine wave is created by plotting a sine function in three-dimensional space. The x and y coordinates represent the horizontal and vertical positions, while the z coordinate represents the amplitude of the sine wave at that point. By varying the values of the x, y, and z coordinates, different 3D sine waves can be created.

3. What is the purpose of visualizing a 3D sine wave?

Visualizing a 3D sine wave can help in understanding the properties and behavior of the sine function in three dimensions. It can also be useful in fields such as physics, engineering, and computer graphics, where sinusoidal functions are commonly used to model real-world phenomena.

4. How does the amplitude affect a 3D sine wave?

The amplitude of a 3D sine wave determines the height of the wave. A larger amplitude will result in a taller wave, while a smaller amplitude will result in a shorter wave. This can be seen by changing the z coordinate in the equation of the 3D sine wave. The higher the z value, the higher the amplitude and the taller the wave.

5. What is the relationship between the frequency and wavelength of a 3D sine wave?

The frequency and wavelength of a 3D sine wave are inversely proportional. This means that as the frequency increases, the wavelength decreases and vice versa. This relationship can be seen by changing the x and y coordinates in the equation of the 3D sine wave. The closer the x and y values are, the higher the frequency and the shorter the wavelength.

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