Frequency of Plane Wave with Magnetic Field Expression in Time Domain

In summary, the expression for the magnetic field of an electric field of a plane wave in air in the time domain is H(t) = y3sin(ωt + 3x + 4z). To find the frequency of the wave, change the variables by setting k = 3x/5 + 4z/5 and solving for k. The denominator of 5 was chosen based on the formula k = sqrt(3^2 + 4^2) = 5. When finding E in phasor form from the given H, the direction will depend on the direction of polarization.
  • #1
magnifik
360
0
The magnetic field expression for an electric field of a plane wave in air in the time domain is H(t) = y3sin(ωt + 3x + 4z). Find the frequency of the wave.

i am having trouble where to begin on this problem. i know how to solve if there is only 1 direction variable (i.e. just x or just z), but since there is an x and z inside the sin, I'm not sure what to do
 
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  • #2
hi magnifik! :smile:

just change the variables … put k = 3x/5 + 4z/5 and see what happens :smile:

(doing it in your head should be enough :wink:)
 
  • #3
tiny-tim said:
hi magnifik! :smile:

just change the variables … put k = 3x/5 + 4z/5 and see what happens :smile:

(doing it in your head should be enough :wink:)

is there a reason you chose the denominator as 5?
 
  • #4
magnifik said:
is there a reason you chose the denominator as 5?

yes! :smile:

and what is it? :wink:
 
  • #5
oh i get it. k = sqrt(3^2 + 4^2) = 5

when i find E in phasor form from the given H, how do i know what direction it should be?
 
Last edited:
  • #6
(just got up :zzz:)
magnifik said:
when i find E in phasor form from the given H, how do i know what direction it should be?

i'm confused :redface:

doesn't it depend on the direction of polarisation? :confused:
 

What is a magnetic field plane wave?

A magnetic field plane wave is a type of electromagnetic wave that is characterized by a uniform magnetic field that oscillates in a plane perpendicular to the direction of propagation.

How is a magnetic field plane wave generated?

A magnetic field plane wave is typically generated by an oscillating electric current or by accelerating charged particles. It can also be generated by changing electric fields or by other electromagnetic waves.

What are the properties of a magnetic field plane wave?

A magnetic field plane wave has a uniform magnetic field that oscillates at a specific frequency and wavelength. It also has a specific direction of propagation and can travel through vacuum or a medium.

What are the applications of magnetic field plane waves?

Magnetic field plane waves have a wide range of applications, including in wireless communication, radar systems, and medical imaging. They are also used in particle accelerators and for studying the properties of materials.

How are magnetic field plane waves different from electric field plane waves?

While both types of waves are part of the electromagnetic spectrum, magnetic field plane waves have a perpendicular magnetic field while electric field plane waves have a perpendicular electric field. They also have different properties and applications.

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