Question regarding Helmoltz equation

  • Context: Graduate 
  • Thread starter Thread starter maverick280857
  • Start date Start date
Click For Summary
SUMMARY

The discussion centers on the Helmoltz equation as it applies to Transverse Magnetic (TM) waves in waveguides, specifically the equation \(\nabla_{t}^{2}E_z + h^2E_z = 0\). It is established that the parameter \(h\) must be real for wave propagation to occur. When the frequency is below the critical frequency, the wave experiences rapid attenuation, represented mathematically as exp[-(Im h)x]. This confirms the necessity of a real \(h\) for effective waveguide operation.

PREREQUISITES
  • Understanding of the Helmoltz equation in electromagnetic theory
  • Familiarity with Transverse Magnetic (TM) wave propagation
  • Knowledge of waveguide theory and critical frequency concepts
  • Basic grasp of complex numbers and their application in wave equations
NEXT STEPS
  • Research the derivation and applications of the Helmoltz equation in electromagnetic contexts
  • Study the behavior of Transverse Magnetic waves in various waveguide configurations
  • Explore the implications of critical frequency on wave propagation in waveguides
  • Learn about attenuation mechanisms in wave propagation and their mathematical representations
USEFUL FOR

Electromagnetic engineers, physicists, and students studying wave propagation in waveguides will benefit from this discussion, particularly those focusing on the Helmoltz equation and its applications in TM wave analysis.

maverick280857
Messages
1,774
Reaction score
5
Hi,

I have the following question regarding the Helmoltz equation in the context of a Transverse Magnetic wave in a waveguide:

[tex]\nabla_{t}^{2}E_z + h^2E_z = 0[/tex]

Question: Is [itex]h[/itex] always real?

([itex]\nabla^{2}_{t}[/itex] denotes the transverse Laplacian operator)

Thanks.
 
Physics news on Phys.org
In a wave guide h is almost always real. It must be real for a wave to propagate.
If the frequency is below the critical frequency, the wave is rapidly attenuated, as
exp[-(Im h)x].
 
Thanks clem.
 

Similar threads

Undergrad Some questions regarding Acoustic wave reflection
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Do electron density waves accompany EM waves in coaxial cables?
  • · Replies 5 ·
Replies
5
Views
1K
Graduate When can I use Helmholtz equation for electromagnetics
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Conservation Laws from Continuity Equations in Fluid Flow
  • · Replies 2 ·
Replies
2
Views
2K
Graduate How to compute the energy of scalar wave equation
  • · Replies 12 ·
Replies
12
Views
2K
Engineering Deriving the Cable Equation (neuroscience) from Fundamental Physics Laws
  • · Replies 1 ·
Replies
1
Views
4K
Graduate Electric and magnetic field lines in a plane wave of finite extent
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Instantaneous electric field solved by extended electrodynamics?
  • · Replies 1 ·
Replies
1
Views
1K
Graduate General equation for hyperbolic motion in a 2D plane -- Help needed please
  • · Replies 14 ·
Replies
14
Views
2K
Graduate Resonant frequencies of liquid in a cylinder
  • · Replies 14 ·
Replies
14
Views
3K