Constructive interference of harmonic electromagnetic waves

In summary, the conversation discusses the possibility of constructive interference between two harmonic electromagnetic waves with different frequencies. The resulting wave cannot be characterized by a single frequency and can be seen as a combination or sum of the two initial waves. However, this only occurs under specific conditions and may not always result in a new and unique electromagnetic wave.
  • #1
MartinG
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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.
 
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  • #2
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.
 
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  • #3
Ibix said:
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?
Superposiciòn de Ondas electromagnéticas armónicas  -  02.jpg
 
  • #4
If your third figure is the sum of the first two, then yes.
 
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  • #5
MartinG said:
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.
 
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  • #6
MartinG said:
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.
 
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Related to Constructive interference of harmonic electromagnetic waves

1. What is constructive interference of harmonic electromagnetic waves?

Constructive interference of harmonic electromagnetic waves occurs when two or more waves with the same frequency and amplitude combine to form a wave with a larger amplitude. This results in a stronger and more intense wave than the individual waves.

2. How does constructive interference differ from destructive interference?

Constructive interference is when waves combine to form a larger amplitude, while destructive interference is when waves cancel each other out and result in a smaller amplitude. In constructive interference, the waves must have the same frequency and amplitude, whereas in destructive interference, the waves can have different frequencies and amplitudes.

3. What is the significance of constructive interference in electromagnetic waves?

Constructive interference is important because it allows for the amplification of electromagnetic waves. This is crucial in many applications, such as wireless communication, where a strong and clear signal is necessary for effective communication.

4. Can constructive interference occur between waves with different frequencies?

No, constructive interference can only occur between waves with the same frequency. This is because for constructive interference to happen, the waves must be in phase, meaning they have the same wavelength and are at the same point in their cycle. Waves with different frequencies will not be in phase and therefore cannot constructively interfere.

5. How is the degree of constructive interference determined?

The degree of constructive interference is determined by the phase difference between the waves. When the waves are in phase, the degree of constructive interference is at its maximum and the resulting wave will have the largest amplitude. As the phase difference increases, the degree of constructive interference decreases until it reaches a point where the waves are completely out of phase and destructive interference occurs.

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