What happens if we clamp a string at both it's ends and pluck it at different distances from one of the ends? Will the frequency of oscillation be the same or will it differ based on the place from where it was plucked?
When you energise a taut string, the following resonant modes of vibration occur:    Plotting on the frequency domain, you can see their corresponding frequencies:    But what is the underlying physical principle? Why does this happen?  Is there any way of explaining it that could be understood by a smart 15 year old?  EDIT: I'm going to give my best attempt so far. Here goes:   We can start with sympathetic resonance. Sounding a particular frequency, a pure sinewave.  And noticing the string resonates sympathetically at the frequency of each harmonic. Say this is explained and understood. Now imagine that plucking a string is equivalent to a burst of white noise, which contains frequencies all the way through the spectrum. This could be approached backwards, by starting with random frequencies and noticing that resultant wave produced looks like white noise.   If the above is scientifically correct, then it restricts the domain of the question.  I would really like to be able to understand it scientifically and also be able to explain it intuitively.  PS Images from
Was "book" to "beek" as "foot" is to "feet"? "Foot" is a curious word in English because it is pluralized in an unusual way; the "oo" in the word is changed to "ee".  Did this once use to be a standard way of pluralizing things in English (or a language that contributed to English), which would mean that the plural of "book" was "beek" instead of "books"?  Or, is "feet" just a one-off? Which tools and technologies are used to build the Stack Exchange Network? What tools and technologies are used to build the Stack Exchange Network?  See also: How to create a rounded cone Schengen Visa Expiration I have a multiple entry 90 days Schengen visa (category C) from 15 March 2014 till 21 Dec 2014.    With this visa I entered The Netherlands on 4 April 2014 and left there on 13 April 2014.    I am planning to re-enter The Netherlands on 19 Dec 2014 and leave there for London (I have a valid UK visa as well) on 21 Dec 2014, at 7 am from Amsterdam.    Am I permitted to stay in The Netherlands on 21 Dec 2014 or should I leave the country on 20 Dec evening itself? What are the C++ rules for calling the base class constructor from a derived class? For example, I know in Java, you must do it as the first line of the subclass constructor (and if you don't, an implicit call to a no-arg super constructor is assumed - giving you a compile error if that's missing). How To Show Node Comment Count in node.tpl? I have had the bright idea of changing my user permissions so as guests cannot see the comments on a node. I have no problems with Views around my site, as they can clearly see there are comments on nodes, and they will be more inclined to register. The problem seems to be when they arrive on my site directly to a node, they don't see any comment, and think "that's a bit crap; let's go."  Is there a way I could show the amount of comments below a node? How can I import Opera bookmarks into Chrome? I am working on a prototype, one function of which is to detect whether an object is "in range" by a few cm. Right now I'm just using an Arduino and a cheap  that operates at 13.56 MHz:    I've successfully gotten it to detect the tag, but only at a distance of about 3-4 cm when the tag is oriented parallel to the antenna.  According to my  , the HF band allows read ranges of between 10 cm and 1 m for passive tags, depending on factors like antenna size, tag size and orientation, and transceiver power.  I realize this inexpensive reader is not up to task as-is, but I'm interested in building something that achieves read ranges of 15-20 cm.  Some criteria:   No need to read multiple tags; only whether one tag is in range or not. No need to write to the tag. Cannot use an active tag.   I'm not experienced with RFID reader construction (yet) but am interested in knowing what I should pursue.  Here are some things I've considered:   Ditch the embedded antenna on the cheap RFID reader and construct my own, larger antenna. I'd need to see if the onboard  is up to the task of providing additional power. Look for a different IC around which to build a reader from scratch. Find a ready-made solution instead of trying to build one (more cost-effective?). Use something other than RFID for simple proximity detection.   I am experienced with microcontrollers and basic electronics, and have made audio and lighting projects, but this is a first with RFID. Since I don't need to read multiple tags, which RFID is suitable for, I've considered maybe some sort of magnet and hall-effect sensor, but the range does not seem adequate. I considered using an ultrasonic proximity detector, but the application calls for detecting the tagged object while ignoring untagged ones (ultrasonic would produce false positives on untagged objects). I've considered some sort of reflective surface placed on the object, and detecting reflected light, but the object orientation is not reliable enough to maintain alignment.  So, in a nutshell, What modifications can I make to my existing reader, or what alternate technology should I pursue to achieve 15-20 cm detection of a passively tagged object?  I plan on connecting whatever proximity detector is used to a microcontroller using SPI. Weird future tense usage I am now reading  book and have noticed a couple of cases of weird (for non-native speaker) future tense usages.   The point of the kata is to train your fingers and your brain. I'll do a kata or two every day, often as part of settling to work. I might do it in Java, or in Ruby, or in Clojure, or in some other language for which I want to maintain my skills.`   The phrase about doing a kata or two every day looks perfect for Present Simple. Why does the authoer use Future Simple instead?   However, a professional also knows that there will be times when he will fail, his risk calculations will be wrong, his abilities will fall short; he'll look in the mirror and see an arrogant fool smiling back at him.   Shouldn't we use Present Simple after when/if in this kind of cases? I am especially curious about this case as sometimes I forget to switch to Present Simple after if/when and I thought it is a critical error (which I didn't expect to see in a book). Preserve blend mode effect when underneath layers are disabled? (Photoshop) I'm a bachelor student majoring in math, and pretty interested in physics. I would like a book to study for classical mechanics, that will prepare me to work through . What books would be good for a beginner? The coupon collectors problem Is GNU's Java Compiler (GCJ) dead? Making leaflet control open by default I'm using leaflet to display a map.  I have a control section that I'd like to be open by default, but I can't find a way to do it through the . Is there a way to do this? Using the fact that $n^3 + 5n$ is divisible by $6$, infer that $n^4 - 2n^3 + 11n^2 + 14n$ is always divisible by $24$ The problem is as stated in the title. I've tried factorization, but it doesn't seem to yield anything. Any help is greatly appreciated. Also please don't use modular arithmetic, thank you. How can I efficiently check the originality of my work? How to know add/edit page in hook_form_alter? I want to know whether form is add/edit in hook_form_alter. In Drupal 7 we can get all these in hook_form_alter.  I tried like this in D7:  function MYMODULE_form_alter(&amp;$form, &amp;$form_state, $form_id) {   // Check pages(s) , don't use $_GET.     if (strpos($form['#action'], '/add/') !== FALSE) {       $page = 'add';     }     if (strpos($form['#action'], '/edit') !== FALSE) {       $page = 'edit';     } }   Here I am getting add/edit in D7. Whereas in D8 I am not getting any it in $form['#actions']. And i don't want to use $_GET. Is there any way to check add/edit page in hook_form_alter. Markdown change: Intra-word emphasis now works There are tons of questions I could maybe post this as an answer to, but before choosing the best one, I'll just post this as an announcement question that can be linked elsewhere. The short story From now on, intra-word emphasis is possible in our Markdown version. That means you can now write  The &quot;V&quot; is for Model**View**Controller. That's un*fricking*believable.  and it renders like this:  The &quot;V&quot; is for ModelViewController. That's unfrickingbelievable.  This only works for asterisks, not for underscores. It works in posts and comments. The reasons There are two big reasons for this. For one thing, this is more or less the behavior of , which we eventually . &quot;More or less&quot; because CommonMark's emphasis behavior is still in flux, and supports a few things that we don't support yet, but at least with this change we're closer. The other reason is languages that don't even have the concept of &quot;words separated by spaces&quot;. See  and  for two examples. This change allow posts in those languages to emphasize words without having to resort to HTML tags. To use an example from the first linked post,  **北京**和**上海**是直辖市。   now renders like this:  北京和上海是直辖市。  Possible issues In the 99% cases, this should only make things better; I've only found very few posts where this change causes unintended bolding/italicizing. And even in those cases, note that the rendered versions of questions and answers are not re-rendered until a post is edited, so this will not affect anything in posts retroactively. Unlike posts, comments are rendered , so this immediately applies to all comments. In most cases this doesn't change anything or actually fixes things. Should you discover a rare case where this breaks an important comment badly, we can always edit it to fix. There's one side effect that I'd like to mention: If you find a great quicksort implementation on GitHub that has a bug that causes a crash when sorting Windows versions, and the author doesn't want to fix it, you may be inclined to say  f**k this s**t   (i.e., &quot;fork this sort&quot;). With intraword emphasis, this would however look like this:  fk this st  So you would have to escape the asterisks (one of them would actually be enough). I'm not worried about this case too much, since if you must put censor-worthy words into a post, you might as well have to jump through a little hoop. Some details This being Meta, there are probably lots of people interested in a more detailed description of the new behavior (don't feel bad if you're not one of them; just skip this section). Here are the major rules regarding intraword-emphasis:  As mentioned, it only applies to asterisks, not underscores. Underscores  this restriction was in place at all; asterisks are much less of a problem.  If a single or double asterisk is supposed to be interpreted as intra-word emphasis, it cannot have punctuation on one side; it actually must be inside a word. An example of an edge case this solves is  It's a web*-based solution. *see Wikipedia for a definition of &quot;web&quot;  where the asterisks after &quot;web&quot; could cause unintended italicizing if there was a second asterisk in the same paragraph somewhere.  For italics, the &quot;inside a word&quot; part of rule 2 is even a bit stricter. For bolding, any word or digit character is allowed; for italics, digits don't work either. That's because the asterisk is often used as a multiplication symbol, so  The game worked in 320200 and 640480 resolution.  wouldn't look right without this restriction.  A minor addition that I made that's only tangentially related to intra-word emphasis is that a sequence of more than three underscores or more than three asterisks will no longer take part in any emphasis. This shouldn't really cause any problems, but fixes some (e.g. the underline in the second blockquote in , while not really visible, is a weird combination of bold and italic underscore characters; after this change, it would just be (more) underscore characters). This behavior also matches CommonMark. What program can I use to decompile a class file? Will I actually get Java code, or is it just JVM assembly code?  On Java performance questions on this site I often see responses from people who have "decompiled" the Java class file to see how the compiler optimizes certain things. Are dual US citizens affected by President Trump's ban on Iran, Iraq, Libya, Somalia, Sudan, Syria, Yemen?