I take two identical lasers, point them at each other from a large distance in space, and fire a pulse from each. The pulse is $N$ wavelengths long. The pulses intersect at the mid point and, for a while, a standing wave is formed by their superposition, and in that standing wave are a series of stationary points at which the E and H fields are 0. There will be $N$ such points, some longer lived than others. However, both pulses are carrying energy, in the E and H fields, and that energy arrives at the final destination, so energy is being transferred, in the form of E and H fields, through points that never have an E or H field. I can do maths, but I'm looking for some sort of physical explanation of what is actually happening to allow this. Can anyone point me in the right direction? I've found a related question which doesn't have answers I can accept (or, for that matter, an accepted answer)  and this one which has the right title but isn't the question I'm asking  This last one doesn't answer the question - the accepted answer instead explains how an additional wave can travel through a pre existing standing wave - I want to know how the two waves forming the standing wave are propagating energy through the nodes.
In a standing wave, how does energy travel past a node?  It should just get reflected. Assume the case of first overtone and you strike the string at a place. How will energy distribute itself?  If it distributes over the whole string, then how is it the wave traveled past a node?  Basically the problem is a standing wave has been set up in the string . Now you strike the string at a place, and this creates a new pulse. Now this pulse will travel past the next node in the string (not the boundary) or will it reflect off even that node and remain confined to a particular region of the string?
Property of $\{0^n, 1^n, \ldots\}$ The differences between adjacent squares are the odd numbers:  0 1 4 9 16 25 …  1 3 5 7  9 …  The differences between adjacent odd numbers are 2 = 2!  I found that this truth is more general: If the differences between adjacent powers of $n$ are written out, and the differences of those differences etc, the $(n+1)$th sequence is {n!, n!, …}  Is this a well-known theorem? Does it have an easy proof? What is the maximum length of a URL in different browsers? What is the maximum length of a URL in different browsers? Does it differ among browsers? Is a maximum URL length part of the HTTP specification? What's the grammar behind "A'warring", from the lyrics of Symphony of Destruction? What's the grammar behind A'warring, from the lyrics of Symphony of Destruction by Megadeth? It's the first time I'm seeing the use of such apostrophe. How can I apply an effect when a player left-clicks/right-clicks with an item in hand? Is there a way so that I make make it when I left click/right click with a certain item it applies an effect? I know that you can apply attributes to wearing armor and things but I want it so when you use the item it applies an effect on your player.  For example, let's say I want something so that when I right click with a certain item (let's say an iron ingot that was given to me) I'll then have a jump boost for 10 seconds. So kinda like a potion in a way.  Is this possible with command blocks/commands/any mods? Do I cast the result of malloc? I did apt-get upgrade it never finishes at this point:  Searching for GRUB installation directory ... found: /boot/grub Searching for default file ... found: /boot/grub/default Testing for an existing GRUB menu.lst file ... found: /boot/grub/menu.lst Searching for splash image ... none found, skipping ... Found kernel: /boot/vmlinuz-3.2.0-24-virtual Updating /boot/grub/menu.lst ... done  You already have a NoLOADER configuration in /etc/grub.conf Running boot loader as requested Running /usr/sbin/grub  ...    The system does not freeze (Ctrl-Z works, I get my console back) just that that /usr/sbin/grub seems to never complete.  What should I do? Add Area 51 Meta to the app Create unmanaged c++ object in c# I am trying to balance underbraces in the equation below, how can I ensure that both underbraces at the same depth?  \begin{equation} y = \underbrace{ \left [ x^2 + r^2 (a^2+\frac{a^{0.3}}{b}) \right]}_\text{growth rate} \times  \underbrace{ C_0}_\text{initial} \end{equation} Show forms in a modal window I have a form and I am using Drupal 7. I need to show this form in a popup when a user clicks a link. The user should then be able to complete the form whilst in the pop up window. I can use anything like  or modals or anything. I just wanted to know which is the better option and what options do I have for Drupal. Why does my front derailleur not work when it is cold? When it is warm outside my front derailleur works just fine. But when it gets colder (40F) the lever on the handle bar does not catch and I can move it without any resistance the whole way without the derailleur shifting.  Update: The wire is not moving and the shifter is a Shimano Deore.  Any idea what can cause that and how to fix it? Should Indicate which Positions I've Already Applied For How to avoid the blackening fruits once they are cut? Apples and bananas start to blacken and sour in taste soon after cutting, which spoils the presentation of dish, especially in fruit salads. How can I avoid this?  Also, does browning impact nutritional value? How to prove $a_1^m + a_2^m + \cdots + a_n^m \geq \frac{1}{a_1} + \frac{1}{a_2} + \cdots + \frac{1}{a_n}$ Installing particular versions when repo has newer versions? Let's have a metapackage which depends on the following packages  Depends: A (=2),  B (=2),  C (=2)   Note the '=' - I want to install these particular versions, not the most recent ones.  Additionally:  B depends on A(>=1)  C depends on B(>=1) and A(>=1)  If the most recent versions of A,B,C in the repository are 2 then this works.  Since I have put version 3 of A and version 3 of B in the repo sudo apt-get install my-meta-package refuses to finish with the following info:  The following packages have unmet dependencies:   my-meta-package: Depends: B (= 2) but 3 is to be installed                    Depends: A (= 2) but 3 is to be installed   If I manually install versions 2 of A and B then the metapackage installs correctly, which strongly suggests that there is no hidden dependency on A3 or B3. This is not a solution for the problem as the metapackage is installed automatically on many machines.  QUESTION: What to do to make sudo apt-get install my-meta-package install versions 2,2,2?  Additionally, is there a way I could get an extended info what actually creates the need for version 3 of A and version 3 of B? I'm trying to run the remove_doubles edit command on multiple selected objects. This is kinda what I got so far...  import bpy   class remDoubles(bpy.types.Operator):     """Remove Doubles on multiple objects"""     bl_label = "Remove Multiple Doubles"     bl_idname = "object.remove_doubles_multi"     bl_options = {'REGISTER', 'UNDO'}      @classmethod     def poll(cls, context):         return len(context.selected_objects) &gt; 0      def execute(self, context):          scene = bpy.context.scene         sel = context.selected_objects          for obj in sel:             scene.objects.active = obj              #do something here             print(obj.name)             bpy.ops.mesh.remove_doubles()          return {"FINISHED"}  myobject = remDoubles()  myobject.execute()   My knowledge about classes isn't too great, please help.  My code needs some work, it just errors out giving a  'TypeError: bpy_struct.new(type): expected a single argument'  But what i intend doing is run through each object applying the remove doubles command for each. Git SSH error: "Connect to host: Bad file number" I am looking for the stuff above, so I can make non-duplicate proposals on area 51. Why Java needs Serializable interface? We work heavily with serialization and having to specify Serializable tag on every object we use is kind of a burden. Especially when it's a 3rd-party class that we can't really change.  The question is: since Serializable is an empty interface and Java provides robust serialization once you add  implements Serializable - why didn't they make everything serializable and that's it?    What am I missing? Subject/Complement Agreement. How to describe problem with "The thing is the objects." In my , I provided the following, problematic,  wording (especially bold italic), and I need help to better understand this issue so I can fix my answer:1          The thing is the books. (Reduced form of Sentence 2.a)         Fundamentally, Sentence 2.a (the so-called "correct" answer), is grammatically defective. Recall there is another grammatical rule: the subject and subject's complement should match in number.    A clarification is needed here. I am not suggesting here, in this EL&amp;U question, that there is any such singular grammatical rule as indicated in the quote above.  The quote continues as follows:     The reduced sentence makes the disagreement between the subject's and complement's plurality obvious. What is one to do? Language is linear and we know "The thing is X" is better than "The thing are X", so we go with the former, which is the subject-verb agreement rule. But what is "the books" then? It must be thought of as a collective noun, even if it doesn't look or feel like one. Forcing something to be a collective noun is related to the idea of notional agreement.   Others noted that grammatically defective is too strongly worded.  There is no such "grammatical rule" for subject/complement agreement.  Please help me understand/improve upon my line of thought here.  I'm stating that Sentence 2.1 presents a fundamental "conflict" or "error" (however one might define error) at some level (morphological, syntax, grammatical, semantic):     The thing is the books.  (Or, "The thing is the objects.")   Based on the "obvious" morphosyntactic plurality conflict, the above sentence feels so wrong that I think many native speakers would think it "simply" grammatically incorrect. However, @F.E. gives counter examples:     And here are some more grammatical examples, where the number of subject and predicative complement don't agree: "They were a problem to us all", "That so-called work of art is simply four pieces of driftwood glued together" (CGEL, page 254-5). As CGEL says: "What is required is semantic compatibility, not syntactic agreement . . .". There are more examples on page 512: "The only thing we need now is some new curtains", "The major asset of the team is its world-class opening bowlers", "Our neighbors are a nuisance", "This gadget is five different tools in one".   I think all the examples given above can be explained as notional agreement.    Question 1: If we explain this phenomena in terms of notional vs syntactic agreement, where does "grammatically correct/incorrect" fit in?  Question 2: Can a simple sentence such as "The thing is the objects." be grammatically incorrect while more complex sentences such as "The thing is four pieces of driftwood glued together." be grammatically correct?  (The answer, in my mind, must be no; this is my conundrum.)  Question 3: Would it be better to say that Sentence 2.a has a low level of (linguistic) ?   Question 4: How about a low level of  and that it's semantically difficult to be (linguistically) ?    Question 5: Do we simply draw a hard line and say "The thing is the objects." is 100% grammatically correct?  I didn't particularly like this option based on intuitive notions of "grammatically correct".    1. Please help me and be kind; I'm trying to improve my understanding. I'm looking for cool, objective advice on how to look at this.  I numbered my questions so they can be easily referenced, if desired.  My preference is the final answer would sufficiently answer all the questions, but of course that can be done explicitly or implicitly.