Constructive interference of harmonic electromagnetic waves

[MartinG]

Hello !

I have a doubt as to how is this case, if it occurs, of the constructive interference of two harmonic electromagnetic waves but of different wavelengths or frequencies between them.

That is, if between the two electromagnetic waves a new and unique electromagnetic wave is created and what characteristics would this new created wave have, such as its frequency, its amplitude and its final or resulting energy.

I thank you for your answers and I send you my regards.

 

[Ibix]

You can superpose waves of different frequencies, yes. Electromagnetism is a linear theory so you may simply add amplitudes. The resulting wave cannot be characterised by a single frequency, much as a chord is not a single note.

 

[MartinG]

You can superpose waves of different frequencies, yes. Electromagnetism is a linear theory so you may simply add amplitudes. The resulting wave cannot be characterised by a single frequency, much as a chord is not a single note.

I will ask you again to see if I understood correctly.

In the superposition of electromagnetic waves, even if they are harmonic waves but of different frequencies, from the two waves a single electromagnetic wave different from the other two would not be formed, but rather we would have a case as shown in the figure I placed, where the resulting wave would it be like the third wave shown in the figure?

 

[Ibix]

If your third figure is the sum of the first two, then yes.

 

[Andy Resnick]

Hello !

I have a doubt as to how is this case, if it occurs, of the constructive interference of two harmonic electromagnetic waves but of different wavelengths or frequencies between them.

That is, if between the two electromagnetic waves a new and unique electromagnetic wave is created and what characteristics would this new created wave have, such as its frequency, its amplitude and its final or resulting energy.

I thank you for your answers and I send you my regards.

It depends on whether or not the two waves are mutually coherent. For example, the output of two different (independent) lasers cannot be combined to produce interference.

 

[sophiecentaur]

In the superposition of electromagnetic waves,

The word "superposition" doesn't imply anything about interaction of the two waves. In a linear medium the displacements at any time and place have no effect on each other. It's only when you actually measure or observe the displacement due to the two waves that you can get a stationary interference effect. There are many places and times for any two waves where the sum is zero, momentarily.

A half way house can be reached with two waves of very nearly the same frequency, when the locations of nulls (fringes) slowly move through space and the resultant, measured in one point in space, will be a 'beat' in time at a frequency which is the difference between the two wave frequencies. Exactly the same thing is happening for any number of waves.