Waveguides and Cavity resonator Equation confusion

In summary, the conversation discusses the differences in the equations used for rectangular wave guides and cavity resonators. The person is confused about why the second derivative is set to different values in each case. The expert explains that this is because the waves behave differently in each type of system, with the wave repeating in a cavity to create a standing wave. The expert also suggests using separation variables and adding boundary conditions to solve the wave equation for a cavity.
  • #1
Dhruv
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Homework Statement


This is not a homework question and I am asking this question out of curiosity. We have been taught rectangular wave guides and cavity resonator recently and I don't want to gulp the wave equations as it is, so the problem that I am facing ( I have written it on paper and uploaded the photo) . Don't know if my question is stupid but it really confuses me .

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The Attempt at a Solution

 

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  • #2
Hello
I don't know exactly what is your problem but I assume you confuse why in rectangular wave guide we set d^2/dz^2=Gama^2 but in cavity d^2/dz^2=-Kz^2?
As you know in the wave guide we transfer a wave in Z direction and it goes through wave guide with it's wave coefficient (Beta) but in cavity a wave repeat simultaneously in the cavity in +Z and -Z direction to create a fix resonator so it should be in sinusoidal form
 
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  • #3
baby_1 said:
Hello
I don't know exactly what is your problem but I assume you confuse why in rectangular wave guide we set d^2/dz^2=Gama^2 but in cavity d^2/dz^2=-Kz^2?

Yes this is what I am confused about. Thank you for reply :) , it helped a lot . So this means I am making changes in equation because I know that in resonator my wave has to be a standing wave rather being a propagating one in +z or -z direction.
 
  • #4
Hello
Yes of course ,However you can try to solve wave equation in cavity and use separation variables to obtain it's answers after that you should add two new boundary condition ( E tangential in EZ(0)=EZ(d)=0 )that only a sinusoidal form can prove that.
 
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  • #5
Thank you :)
 

1. What is a waveguide?

A waveguide is a structure that is used to guide and transmit electromagnetic waves, typically in the microwave and radio frequency range. It is a hollow metal tube or pipe with a specific shape and size to confine and direct the propagation of electromagnetic waves.

2. How does a waveguide work?

A waveguide works by confining and guiding electromagnetic waves within its structure. The walls of the waveguide reflect and guide the waves along its length, similar to how a pipe guides the flow of water. This allows the wave to travel with minimal loss and distortion, making it an ideal medium for transmitting electromagnetic signals.

3. What is the difference between a waveguide and a cavity resonator?

A waveguide is a structure that guides and transmits electromagnetic waves, while a cavity resonator is a device that stores and amplifies electromagnetic energy in the form of resonant standing waves. A cavity resonator typically consists of a hollow cavity made of conductive material, while a waveguide can be made of various materials and shapes.

4. What is the cavity resonator equation?

The cavity resonator equation is a mathematical formula that describes the resonance frequencies of a cavity resonator. It takes into account the dimensions and material properties of the cavity to determine the resonant frequencies at which it will store and amplify electromagnetic energy.

5. Why is there confusion between waveguides and cavity resonator equations?

There may be confusion between waveguides and cavity resonator equations because they both involve the propagation and manipulation of electromagnetic waves. Additionally, some of the concepts and equations used in the study of waveguides may also apply to cavity resonators. However, it is important to understand the distinct differences between the two in order to properly apply their equations and principles.

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