Planar wave expansion cancelling through interference

[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]

Oh and thank you for your answers in advance! :)

 

[berkeman]

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?

 

[Hache]

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?

 

[berkeman]

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)

 

[Hache]

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?

 

[tech99]

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.