# Planar wave expansion cancelling through interference

• Hache
In summary: The wave is only 2 cycles long, so it is not a real wave. The particles are stationary at the interference points, and the wave has nowhere to go.

#### Hache

Hello everyone!

In a hypothetical 3D space, with no boundaries around, homogeneous normal conditions, what would happen to the advancement of a planar wave front produced at t=0 with 2cycles in length, λ=3.5m, moving with vector speed "c-arrow=1i-arrow" if an identical planar wave of 2cycles in length which origin is x(7,0) moving with vector speed "c-arrow=-1i-arrow" is produced also at t=0. Would the planar waves just cancel each other between the origins and disperse? or they would cancel each other between the origins but they would keep advancing in their respective directions? Maybe it's a dumb question but I can't figure it out.

Hache said:
Hello everyone!

In a hypothetical 3D space, with no boundaries around, homogeneous normal conditions, what would happen to the advancement of a planar wave front produced at t=0 with 2cycles in length, λ=3.5m, moving with vector speed "c-arrow=1i-arrow" if an identical planar wave of 2cycles in length which origin is x(7,0) moving with vector speed "c-arrow=-1i-arrow" is produced also at t=0. Would the planar waves just cancel each other between the origins and disperse? or they would cancel each other between the origins but they would keep advancing in their respective directions? Maybe it's a dumb question but I can't figure it out.

Welcome to the PF.

Could you clarify the situation a bit more please? what is x(7,0)? Do you mean a location (x,y) = (7,0)? What is the position of the origin of the first wave? And are you using vectors i and j to represent unit vectors in the x and y directions?

Thank you! Glad to be here!

Sorry, I wrote the post too fast. Yes I meant x,y (7,0) and i and j are unit vectors in x and y directions. I just wanted to make very clear that the waves are moving in opposite directions and they would start with φ=0º that they are sinusoidal and they would interfere between the origins. But will the waves continue their advancement... or will they be stopped by the interference?

Hache said:
Thank you! Glad to be here!

Sorry, I wrote the post too fast. Yes I meant x,y (7,0) and i and j are unit vectors in x and y directions. I just wanted to make very clear that the waves are moving in opposite directions and they would start with φ=0º that they are sinusoidal and they would interfere between the origins. But will the waves continue their advancement... or will they be stopped by the interference?

They will continue on. The interference is localized, and does not affect the waves. (unless their amplitudes are large enough to cause non-linear interactions between them, which I don't think is what you are asking)

Well, those non-linear interactions are very interesting though and would like to read about them. The answer is what I expected, but it's counterintuitive. Since this is a mechanical wave, the particle movement at the interference is 0. The wave is finite and only 2 cycles long. Therefore the question is, how can the wave keep expanding after the interference if there was no net particle movement and therefore no compression/rarefaction?

I the case you have described, the waves are planar, so not spreading out. They will be completely intercepted by each others "origins", which I presume to be something like a very large piston, for instance. You end up with a standing wave system.With a standing wave, we do not see a flow of energy, and that is why you see zero particle movement.

## 1. What is planar wave expansion cancelling through interference?

Planar wave expansion cancelling through interference is a phenomenon in which two or more plane waves with different amplitudes and phases interact with each other, resulting in the cancellation of certain frequency components and the enhancement of others. This can occur when the waves have the same frequency and are traveling in the same direction, leading to destructive interference.

## 2. How does planar wave expansion cancelling through interference work?

In planar wave expansion cancelling through interference, the waves interfere with each other in such a way that the resulting wave has a different amplitude and phase than the individual waves. This can be explained using the principle of superposition, where the amplitudes of the waves are added together at each point in space. If the amplitudes of the waves are equal and opposite, they cancel each other out.

## 3. What are the practical applications of planar wave expansion cancelling through interference?

Planar wave expansion cancelling through interference has many practical applications, such as in noise cancellation technology, where sound waves with equal and opposite amplitudes are used to cancel out unwanted noise. It is also used in radio and telecommunications to reduce interference and improve signal quality.

## 4. Can planar wave expansion cancelling through interference occur in three dimensions?

While the term "planar" suggests that this phenomenon only occurs in two dimensions, it can also occur in three dimensions. This is known as spatial wave expansion cancelling through interference, where the waves interact in a three-dimensional space and cause cancellation of certain frequency components.

## 5. How is planar wave expansion cancelling through interference different from other types of interference?

Planar wave expansion cancelling is a specific type of interference that occurs between plane waves with different amplitudes and phases. Other types of interference, such as constructive interference and diffraction, involve the interaction of waves with different properties, such as different frequencies or directions of propagation.