Understanding Interference: Wave A & Wave B

[franco1991]

Interference Question:

I'm trying to understand interference, I get the basic concept, that when two EM waves are superposed the resultant's amplitude of the vector sum of each original wave's respective amplitude. It's the following the creates confusion.

Picture the figure below. Wave A is a laser beam, and is traveling horizontally. Wave B is also a laser,m but has a propagation-path that intersects Wave A, such that at that point they are susceptible to interference (they are of the same frequency).

http://www.quia.com/files/quia/users/petetm/intersecting-lines.bmp

In the image, assume the waves are traveling in the directions their right-most arrows indicate (and that they travel in the same *general* direction), the actual angle is arbitrary, so long as it is small enough to ensure the waves superpose at the intersection-point.

Example 1: The waves, at the point of intersection, are 180 degrees out of phase, thus inducing destructive interference. If Wave A (horizontal) has an amplitude of 2, and Wave B an amplitude of 1, the resultant will have an amplitude of 1 (A= 2-1, A=1). But, does that mean that the output of wave A (the parts that propagate AFTER (to the right of) the point x (the point of intersection) will be a wave traveling along the path of Wave A and that has an amplitude of 1? Is it that the wave-train that has the larger amplitude (wave A in this case) will always be the one that retains a positive amplitude (in the case where destructive interference doesn't fully equal an amplitude of 0)? And likewise, if Wave B has an amp. of 2 and wave A had an amp of 1, would it be that propagation path of wave B that the resultant (with an amp of 1) travels along? Is this how interference works?

2nd question: Is there any way to make it so that both waves interfere destructively, but neither are fully negated, such that after that point of intersection both Wave A and Wave B have a lower amplitude? Perhaps thru not being fully out of phase, but out of phase by a fraction of a cycle? Or will this just reduce the magnitude of the decrease in the resultant's amplitude?

Details: I've heard that they interfere at that point, but then continue on their normal paths. But this doesn't seem to make sense; the resultant must travel in some direction, so wouldn't it be the one with the larger amplitude? Also, the first wave (which is negated in destructive interference) can't continue propagation, it was canceled out, a wave with amp = 0 can't propagate.

I haven't been able to get a clear answer from other forums, so if someone could either verify or deny, and if deny explain exactly just what happens in these cases then, It would be very very much appreciated.

 

[Dale]

Details: I've heard that they interfere at that point, but then continue on their normal paths. But this doesn't seem to make sense; the resultant must travel in some direction, so wouldn't it be the one with the larger amplitude?

This is correct.

The thing is that the resultant is not a simple wave. For example, consider a plane wave moving in the +z direction with E field along the +x and B field along the +y direction. Suppose it interferes with a wave moving in the +y direction with an E field along the +x and a B field along the -z direction. Then the E fields interfere constructively and the B fields interfere destructively and the superposition is no longer simply a plane wave since the B field is not in the correct relationship with the E field for a wave.

 

[franco1991]

Thank you for the response, but I'm still not sure I understand.

1.) Why in particular did you use plane waves in your example? Would the same thing happen in these waveforms, which are beams of finite extent rather than plane waves?

2.) So, are you saying that the two examples given under heading "example one" - i.e where the resultant has a definitive amplitude which is the difference between the original waves' amplitudes, traveling along the same bath of either Wave A or wave B respectively, are impossible? That it will never be such?

2.) Why can't Waves A and B have E and B field components 'propagating' in the same axis, so there is no discrepancy causing the E and B fields to not be in the proper relation with each other?
Or are you saying it is impossible b.c all 3 axes cannot be equal in both waves (i.e E field component of Wave A moving in the same axis as the E field component of Wave B) , b.c if they were they would be perfectly superposed and not intersecting at an angle?
If this is the case, why isn't it possible to have the E and B fields (and propagation direction) in both waves be in the same axis, just traveling at slightly different directions in one or more of the axes (like the axis corresponding to their propagation direction), so the E and B fields still superpose and are still in proper relation to each other for the result to quality as a resultant EM wave?

Basically, what I'm asking is 1.) Why can't you negate the discrepancy by simply making the E and B fields and propagation direction of each respective wave in synch and of corresponding axes? and 2.) If the answer to 1 is that if they all corresponded, it wouldn't be intersecting at an angle but superposed why can't you resolve this by having the E and B fields of each respective wave in synch and in the same axis, and rather the propagation direction the one out of synch, rather than the E and B fields.

Sorry for the abundance of question, I just really want to understand this.

 

[Antiphon]

Consider the term "superposition" instead of interference. Interference does not mean interaction. The wave pass through one another like ghosts.

 

[technician]

I agree with Antiphon, the waves pass through each other.
It is most easily seen with 2 (or more) water waves. Where they cross superposition/interference occurs.

 

[Dale]

1.) Why in particular did you use plane waves in your example? Would the same thing happen in these waveforms, which are beams of finite extent rather than plane waves?

If you pick a small region a plane wave becomes a good approximation for many waves. I picked it because it is the simplest useful example.

2.) So, are you saying that the two examples given under heading "example one" - i.e where the resultant has a definitive amplitude which is the difference between the original waves' amplitudes, traveling along the same bath of either Wave A or wave B respectively, are impossible? That it will never be such?

Correct. In the region of interference, if the E field cancels the B field will add constructively, and the resultant is not, by itself, a traveling wave.

2.) Why can't Waves A and B have E and B field components 'propagating' in the same axis, so there is no discrepancy causing the E and B fields to not be in the proper relation with each other?

Look up the Poynting vector. It describes the relationship between the E and B fields and the direction of propagation. Fix any two, and the third is uniquely determined.

 

[Studiot]

ψ

I get the basic concept, that when two EM waves are superposed the resultant's amplitude of the vector sum of each original wave's respective amplitude.

This might be the source of some of your confusion.

The amplitude of a wave is the peak value only. It is a constant for a single wave.

y = Asin(wt+ψ)

A is the amplitude.

ψ is the phase angle.

y is the instantaneous value.

So for two waves we have

y₁= A₁sin(wt+ψ₁)

and

y₂= A₂sin(wt+ψ₂)

It is the instantaneously values y₁ and y₂ that add vectorially.

go well