Cartesian Co-ordinates of Plane Wave

In summary, the conversation discusses finding the expression in Cartesian coordinates for a plane wave with amplitude A and frequency ω propagating in the direction of the vector k, which lies on a line drawn from the origin to the point (4,2,1). There is some uncertainty about the correct expression, with one person suggesting it should just be A*e^(i(kr –ωt)) and others considering other possibilities such as E*e^(i(4x+2y+z –ωt)). The group also discusses finding the components of k, with k_x=4k/sqrt(21) being one possible solution.
  • #1
Ayame17
44
0
Write an expression in Cartesian coordinates for a plane wave of amplitude A and frequency ω propagating in the direction of the vector k which, in turn, lies on a line drawn from the origin to the point (4,2,1).



Well, we know plane wave is E(r,t)= E*e^(i(kr –ωt)) where E = A*(direction of propagation) for a 3D wave. However, we're not entirely sure where to go now. One of our friends believes it should just be A*e^(i(kr –ωt)), ie just the amplitude , not propagation as above. We also think that it might be E*e^(i(4x+2y+z –ωt)), as k*r should equal 4x+2y+z. Are we anywhere near being along the right lines?
 
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  • #2
No.
k.r means xk_x+yk_y+zk_z.
You need to find the components of k.
k_x=4k/sqrt(21), etc.
 

FAQ: Cartesian Co-ordinates of Plane Wave

What are Cartesian co-ordinates of plane wave?

Cartesian co-ordinates of plane wave refer to the use of the Cartesian coordinate system to describe the direction and magnitude of a plane wave. This system uses three orthogonal axes (x, y, and z) to represent the position of a point in space.

What is the physical meaning of the Cartesian co-ordinates of plane wave?

The Cartesian co-ordinates of plane wave represent the direction and magnitude of the electric and magnetic fields of the wave. This allows us to visualize and understand the behavior of electromagnetic waves in three-dimensional space.

How do you convert from polar to Cartesian co-ordinates of plane wave?

To convert from polar to Cartesian co-ordinates of plane wave, you can use the following equations:

x = r * cos(theta)

y = r * sin(theta)

Where r is the distance from the origin and theta is the angle from the positive x-axis.

Why are Cartesian co-ordinates of plane wave important in physics?

Cartesian co-ordinates of plane wave are important in physics because they allow us to mathematically describe the behavior of plane waves. This is crucial in understanding and predicting the behavior of electromagnetic waves, which are essential in many fields of physics such as optics and electromagnetism.

Can you use Cartesian co-ordinates of plane wave to describe other types of waves?

Yes, Cartesian co-ordinates can be used to describe other types of waves, such as sound waves and water waves. However, the equations and physical interpretations may differ depending on the type of wave being described.

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