2 wave pulses identical in shape but inverted with respect to each other are produced at the two ends of a stretched string. at an instant when the pulses reach the middle,the string becomes completely straight. what happens to the energy of the 2 pulses?
134098
Such a pulse produces a standing wave. In such standing wave energy is not transferred from one place to another.\n\nAt each instant we see a wave, but the waves do not move.\n\nThere are certain points which never move, they are called nodes.\n\nBut between nodes the points are displaced.\n\nAt one instant, all points are motion less.\n\nAfter this instant, points that previously went up will now come down and vice versa.\n\nExcept the nodal points, all points are oscillating between potential and kinetic energy. \n\nThe maximum displacement corresponds to potential energy and the mean position corresponds to kinetic energy.\n\nAt the instant when all points are motion less, ALL POINTS EXCEPT THE NODAL POINTS have kinetic energy, by which they continue their oscillation.
468851
each of the particles would have 1/2 the energy of the spring, 30 j each.  They would move at different speeds, c moves slower than d, but energy 1/2 mv^2 would be the same.
535592
You've lost the point of the equation.  Squaring the speed of light will give you the energy released, not an enhanced speed of light.
321295
Be careful with your statement.  The electrons do not act like both a wave and particle at the same time!  They act like one or the other.\n\nWhen you are not "watching" the electrons, they exhibit wave like behavior because they hit on the screen only in the spots that would correspond to a bright fringe for light.  But, that isn't the coolest part.  \n\nFirst: you can shoot one electron at a time, and each time, each electron will hit at a spot that would be a bright fringe, if you were to shoot light with the same wavelength through two slits.  Now, cover one of the slits and shoot one electron at a time, and the pattern will shift to that of a single slit diffraction. \n\nQuestion: How does the electron "know" if there are two slits or one slit, so that it hits the correct spot on the screen?  Answer: if there are two slits open, it goes through both slits on its way to the screen!  In essence, it interferes with itself!  This is what is known as the sum of histories, where the electron is said to take every path possible on its way to the screen.  \n\nOf course, you might object and say when I shoot a cannon ball into the air, it only takes one path: the parabolic curve.  So, why does an electron take every path and the cannon ball does not?  This is the essence of quantum physics: these bizzare happenings occur with the very small.  However, the sum of histories can still be applied to a cannon ball, but guess what?  All paths cancel except for the parabolic path it will always take on Earth.  For the electron, each path has equal probability, so they do not cancel, thus it goes through both slits at the same time.\n\nSecond: If you try to "watch" the electron go through both slits by using an instrument, the electron stops acting like a wave, and behaves like a particle.  It hits the screen like a particle should.  Stop "watching" it and the pattern goes right back to that of wave interference!\n\nIt's as if nature will not allow us to see such bizarre things.
523279
I expect that you have the data on stretch as a result of tension. \na) The object is just at rest. Tension, T = W = m*g.\n\nb) T = W + m*a\n\nc) Tmax = W + m*a
442007
The choice of the violin was a bit unfortunate since violins have a special frequency response that is not a parabolic wave when properly bowed:  \nhttp://plus.maths.org/issue31/features/woodhouse/\n\nWell, that may not be the point here since the author of the book probably assumed that the string follows the harmonic frequency behavior as described by:\n\nf=sqrt(T/u)/(2*L)\nwhere T is the tension\nu is the linear mass (Mass per unit length)\nL is the length\nAnd f is the frequency harmonic.\n\nThe act of "fingering" the string is to depress it and thereby change the length.  You can likely assume that this has negligible effect on the tension of the string.  So if when fingered the new l = 2L/3\nyou just plug that into the equation and solve using a ratio:\n\nf=K/L\nf'=3K/2L\nf"/f=3/2\n\nj
9476
The energy isn't destroyed, but it is reorganized into different forms.  Think of it this way: Imagine you have a bunch of fridge magnets with words on them, and you arrange them into a brilliant poem.  When you come back later, someone else has rearranged the magnets.  All of the magnets have been "conserved"-- they're still there, and they're just as magnetty as ever-- but the particular shape that they were in when they were your brilliant poem is unrecoverable.  Sorry. <3
612105
The wave length is the distance between two  consecutive points which are in same phase.\n\nThe wave pattern repeats itself after one wavelength.\n\nThus we can consider this as one cycle of operation. \n\nOne cycle corresponds to 2pi radian or 360 degree.\n\nThus a wave length ( Lambda) corresponds to 2pi radian\n\nAny orbitrary length l corresponds to( 2 pi/ lambda ) x l\n\nThe path differnce l is equivalent to a phase difference of  ( 2 pi/ lambda ) x l\n\nA phase difference of Theta corresponds to a path difference of  ( Lambda/2pi ) x theta.
66928
Lots of wave phenomenona exhibit both longitudinal and transverse components simultaneously. For example,  \n\na. Seismic waves have both longitudinal and transverse components, the P and S waves. Any physical medium can support both types of mechanical wave (see reference 6 for both longitudinal and transverse waves in a piezoelectric material). \n\nb. Ocean surface waves have both transverse and longitudinal components, and particles near the surface of the ocean execute a retrograde elliptical motion as a result (similar to the Rayleigh wave in seismology). \n\nc. In 2002, the discovery of a trapped boundary seismic wave with both longitudinal and transverse components that travels along the ocean bottom was announced (see reference 7).\n\nWhat about light and de Broglie waves?\n\nThe electromagnetic energy (light) we are familiar with is composed of transverse waves (reference 1). For example, light can be polarized, which is a feature of transverse waves. The spin states of the photon viewed as a particle are analagous to the polarization of an electromagnetic wave. However, the polarization of a photon is circular (either left or right), which is a more accurate way to visualize photon spin states (see reference 8, 9). \n\nNormally, the longitudinal component of photons corresponds to a nonphysical gauge (see reference 2). In standard theory, as long as the photons travel at the speed of light, they cannot have a longitudinal component. However, virtual photons have a nonzero-rest mass, and travel at less than the speed of light, so they can have a longitudinal component (references 3, 4). \n\nA Russian journal article that discusses the possibility of longitudinal electromagnetic waves in any medium can be found in reference 12. \n\nThe de Broglie waves of matter that are the basis of quantum mechanics also have spin states, something like a transverse wave (as shown in the Stern-Gerlach experiment; see reference 8). The Schrodinger equation for the propagation of these waves is a scalar equation for the wave function (whose modulus squared gives the probability of finding a particle at a given position in time and space, for example), so it does not give much indication of the nature of the wave itself. However, the more general relativistic Dirac equation is a vector PDE (or more properly, a spinor PDE), and the wavefunction in this case is a 4-dimensional spinor. Plane-wave solutions of the Dirac equation admit both positive and negative energy eigenvalues, corresponding to 2 different spin states.\n\nIn some conditions, such as having discrete time, it is possible to find longitudinal solutions called "oscillons" to the Dirac equation (see reference 10). Dirac's interpretation of the lack of time-like longitudinal solutions to his equation was connected to the existence of the time-energy uncertainty relation. As pointed out in reference 11, there are space-like longitudinal solutions to the Dirac equations. \n\nNikola Tesla, who appears to have headed off into pseudoscience the last few years of his career, believed that photons in a vacuum travel as a longitudinal wave.Nikola Tesla wrote: " I showed that the universal medium is a gaseous body in which only longitudinal pulses can be propagated, involving alternating compressions and expansions similar to those produced by sound waves in the air. Thus, a wireless transmitter does not propagate Hertz waves, which are a myth, but sound waves in the ether, behaving in every respect like those in the air, except that, owing to the great elastic force and extremely small density of the medium, their speed is that of light." \n\n(Source: "Pioneer Radio Engineer Gives Views on Power", published in the New York Herald Tribune, Sept. 11, 1932, [2, p.94 ]. )\n\nIn summary, I would say that longitudinal electromagnetic fields and longitudinal solutions to the Dirac equation governing de Broglie waves are still somewhat speculative, but the in
326684
Depends on the pair produced.  For example, in one case the answer is (a) mass is creeated at the expense of energy.  More commonly referred to as "pair production", this process occurs when a high energy photon (usually a photon, but it could be any bosonic field) creates a particle and it's anti-particle, most usually we're talking about an electron and a positron.  The photonic energy and momentum are both conserved during the process, where the total energy and momenta of the pair sum to the energy and momentum of the original photon.\n\nA similar process occurs when a photon under the action of a strong polarization field splits into 2 photons of higher wavelengths.  This is known as optical parametric oscillation, but in this process matter is neither created or destroyed since the resultant pair are both massless photons, they just have different energies.\n\nThe thing to keep in mind is that matter and energy are interchangeable quantities.  If matter is created, then the energy will drop in the result.  Energy cannot be created, but mass can become energy, and vice versa.
278783
i don't know... this is all theoretical, and i would guess that this either \na- does not and cannot happen, or\nb- happens all the time and is therefore not something to be concerned about\n\ndid you read The Elegant Universe by Brian Greene? or Fabric of the Cosmos? (same author) \nI suggest these for further understanding of the string theory.... without having to consider the complexities of the mathematics behind it.
596743
The top answer is incorrect.  In both cases, the current woul go on infiniitely, because energy will keep on traveling, but the current will get weaker and weaker, because it will keep spreading aparty, until the ammount of current in negligeble.\n\nHope this helps.
308728
it would double. imagine you stretch a spring with constant k a distance x using force f=kx. now while you are holding the end at displacement x, also hold the middle of the spring, which has been displaced x/2. now cut the spring in the middle while holding it, so the second half falls off and the first half is still stretched. since the first half is not stretched any farther than it was before, the force is the same. the displacement, however is x/2. so, the new spring constant is 2k.\n\nspring constant is really a misnomer; its not constant for the material, but only for that spring of that length. it should really be given as a constant independent of the length of the spring, constant per unit length, but alas it is not.
453814
The wavelength is shorter but the speed is the same, so the oscillations in the field are at a higher frequency, and that means it takes more energy to create them and they provide more energy when they are absorbed. Something like that.
218718
Since Einstein is rather inconveniently dead at the moment, I'll have to answer.  \n\n\nWhy we can't simply have a half a photon that goes undetected is a good question, from the information presented in that article, but a reason it can't work like that:\n\nThe energy of light is related to its wavelength, so if a photon split into two equal halves, then each would have twice the wavelength.  Of course, I'm kinda cheating here, since the relationship between energy and wavelength is one of the rules of photon quantization.  However, there's a very good theoretical reason for this: the ultraviolet catastophe.   See links below.\n\nThe "twin" in this case is really the same photon.  So, this is an example of superposition, which is similar to entanglement.  Entanglement is basically when a set of particles are put into superposition such that the outcome of a measurement on one depends on the measurement of the other.  In this case, the photon is simply in two possible paths through the beamsplitter until such time as it's measured.  Superposition is said to occur whenever a particle is put in a state such that it can have more than one observable outcome if measured.  Until such time that the photon hits one detector or another, it's both reflected off the mirror *and* passed through the mirror.  Yes, it seems like it really ougth to be one or another, doesn't it?  However, QM doesn't work that way.   \n\n\nIf there were three paths...  well, then there would be three paths.  It depends on what the detectors and other optical devices put in the path can do as far as how this would affect the whole behaviour of the system. \n\nThe example given there is the classic "interaction free measurement" trick, also sometimes called quantum interrogation.  It's an important function in ideas about quantum computing since it allows information about states to be retrieved without upsetting entangled states.\n\nIt's getting rather late in my current timezone, and I haven't had dinner yet.  I'll answer in more detail and answer your additional comments once I get some dinner in me.\n\nOK, a few additions...\n\nThe screen placed in either path breaks the single particle interference and gives rise to the possibility of detector B finding the photon, but it doesn't rule out the photon still ending up at detector A, and it also gives rise to the possibility that the photon gets absorbed by the screen.  However, the amazing thing is that if the photon does show up at detector B, then it will tell us that something is located in the optical path without ever having interacted with it.  Presto!  An interaction free measurement.  So, this both shows some interesting possibilities for quantum measurement tricks, which have implications for quantum computing, and shows one of the achilles' heels of the technique.  In this case we can do something which is impossible in a classical physics sense, but we also have three possible outcomes of the experiment, only one of which actually does anything interesting.  So, there are a lot of issues in the development of quantum computing that hinge on the ability to take advantage of these strange effects, but also give us good reliability of the answer.  Taking this trivial example, what we'd need is to develop a more complicated system in which the interaction free measurement effect occurs not 1/4 of the time (half the time the photon is absorbed, if not absorbed, half the time it ends up at A, which tells us nothing) but almost every time.  There are ways to do this, but it gets very complicated very quickly.  \n\nAs for how you get a single photon to work with in the first place...   We currently don't have the technology to simply conjure up a single photon reliably.  There are certainly hypothetical ways it can be done, but right now you just take a brief low intensity laser pulse, pass it through a filter that will
637530
An inverter by itself can only take one logic state and invert it to another.   For example, a logic 1 on the input would be inverted to a logic 0 and vice-versa.  This logic state will be held until the input's logic state changes.\n\nTo get a pulse, you need the logic state to invert only temporarly before returning to its original state. \n\nTherefore, an inverter by itself cannot be used to generate a pulse.  You could use a simple RC (resistor-capacitor) network on the input of an inverter to generate a pulse though, but it would not be repetitive.
405038
If the two lasers have the same frequency and you pointed them right into each other a thing called a node would form. Which is the cancelation of the wave. The red light would no longer visible because that light hase been deformed by deconstructive interference due to the only single frequency laser that was pointed at it. The node would go all the way into the origin of the other laser and there would be nothing but blankness. The instant the lasers stop interfering with each other the laser will come back to its original state.