What is Modes: Definition and 281 Discussions

A normal mode of an oscillating system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation. The free motion described by the normal modes takes place at fixed frequencies. These fixed frequencies of the normal modes of a system are known as its natural frequencies or resonant frequencies. A physical object, such as a building, bridge, or molecule, has a set of normal modes and their natural frequencies that depend on its structure, materials and boundary conditions. In music, normal modes of vibrating instruments (strings, air pipes, drums, etc.) are called "harmonics" or "overtones".
The most general motion of a system is a superposition of its normal modes. The modes are normal in the sense that they can move independently, that is to say that an excitation of one mode will never cause motion of a different mode. In mathematical terms, normal modes are orthogonal to each other.

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  1. binbagsss

    W+ decay modes neglect mass branching ratiosQ

    Homework Statement The question is that the decay modes for the ##W+## boson are , ##e^+ v_{e}, \mu^+ v_{\mu}, \tau^+ v_{\tau}, ud', cs' ##, where a ' denotes a anitquark, neglecting the masses of the decay products estimate the branching ratios of the ##W+##? Homework Equations N/A The...
  2. W

    How many acoustic and optical modes are there in a 3D crystal with p atoms?

    Homework Statement Homework EquationsThe Attempt at a Solution Since it's 3D, I assume there's at least 3 acoustic modes and 3 optical modes? After all, the soundwaves/phonons must be able to travel in all directions. Further on, I know both longitudinal and transverse modes are possible...
  3. G

    Difference in proof between TE and TM modes

    I'm a little confused regarding the maths of TE and TM modes. Solving the following system for TE (which derives from Ey(x, z, t) = Em(x) = exp[i(ωt-βz)] ): Asin(px) + Bcos(px) , -d/2 < x <d/2 Cexp(-qx), x>d/2 Dexp(qx), x<-d/2 we conclude in two types of solutions for TE modes: symmetric...
  4. R

    How does increasing temperature increase modes?

    Homework Statement Explain why the number of modes per particle increases with increasing temperature for all gases (except monatomic gases). Homework EquationsThe Attempt at a Solution I am trying to use an energy argument but to be honest, I don't understand the excited state vs rest state...
  5. H

    Normal modes of continuous systems

    Homework Statement A room has two opposing walls which are tiled. The remaining walls, floors, and ceiling are lined with sound-absorbent material. The lowest frequency for which the room is acoustically resonant is 50Hz. (a) Complex noise occurs in the room which excites only the lowest two...
  6. L

    Molecular Orbital & Normal Modes

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  7. vead

    TEM TE and TM Modes for Waveguides ?

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  8. S

    Guess Decay Modes: A, Z, Mass Diff MeV

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  9. G

    Structural Vibrations Analysis & Simulation

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  10. Spinnor

    Casimir effect excludes photon modes*, same for two slit interferometer?

    Can we say that a point light source (turned off) together with a two slit interferometer and say a photographic plate detector exclude certain photon modes? Light does not go to certain parts of the photographic plate so can we say that the source (turned off), the interferometer, and the...
  11. PhysicsKid0123

    Why are normal modes important when analyzing waves or oscillations?

    Why are they important? I've been learning about them quite a bit and have no idea why they are significant. What is the motivation for their discovery, their use, or even their mention in physics for that matter. All I really know is that when you look/have solutions with the same angular...
  12. Z

    What is the lower limit of frequency range of acoustic phonon modes?

    Good day everyone. I would like to know about the lower limit of the frequency range of active acoustic phonon modes. Textbooks say it can reach zero. But I am curious about whether it can be very small, such as 1 micro volt or the like. Would a phonon mode of so small energy be of any...
  13. W

    Degeneracies in Optical Modes in relation to Heat Capacity in a Solid

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  14. sergiokapone

    Harmonic oscillations of the electromechanical system (normal modes)

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  15. W

    Relating molecules, atoms to number of optical branches (modes)

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  16. D

    Normal modes of electromagnetic field

    Hey guys, I'm trying to understand the properties of normal modes of the electromagnetic field inside an arbitrary cavity, but I'm having some trouble. By definition, for a normal mode we have \mathbf{E}(\mathbf{x},t) = \mathbf{E}_0 (\mathbf{x}) e^{i \omega_1 t} and \mathbf{B}(\mathbf{x},t) =...
  17. J

    Frequency for Vibration Modes of a Square Membrane

    So the equation to obtain the frequency of the modes of a square membrane is something like ω m,n = ∏ [(m/a)^2 + (n/b)^2]^(1/2) This equation can be used to get the frequency for Modes such as (2,1) and (1,2). How do I get the frequency for such modes as (2,1)+(1,2) and (2,1)-(1,2) ...
  18. R

    Modes - physical meaning and use

    Modes is usually encountered in physics when we study wave propagation of any sort. Every frequency has n number of modes depending on boundary conditions - I know that much but, find it difficult to relate to so many concepts in which modes get mentioned and they baffle me at times. I want to...
  19. J

    Help plotting interacting Turing modes

    Hello, everybody. I'm trying to replicate plots from Yang et al. 2002. Spatial resonances and superposition patterns in a reaction-diffusion model with interacting Turing modes. Phys. Rev. 88(20) using Mathematica, to explore specifically under what parameter values the pattern of...
  20. S

    Degenerate Modes in Photonic Crystal Cavities: Examining Resonant Frequencies

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  21. K

    Why do TEM modes need two conductors to propagate?

    Why do we need two conducting surfaces to allow TEM modes to propagate through a waveguide? Why can we not propagate TEM waves through a single conducting waveguide?
  22. R

    Can somebody explain boundary conditions, for normal modes, on a wire?

    I don't really understand boundary conditions and I've been trying to research it for ages now but to no real avail. I understand what boundary conditions are, I think. You need them along with the initial conditions of a wire/string in order to describe the shape of motion of the string. I...
  23. R

    Form of the displacement, y(x,t), for the normal modes of a string

    Homework Statement The displacement, y(x; t), of a tight string of length, L, satisfies the conditions y(0, t) = \frac{\delta y}{\delta x}(L,t) = 0 The wave velocity in the string is v. a) Explain what is meant by a normal mode. Give the form of the displacement, y(x; t), for the normal...
  24. K

    Number of modes for a 2d crystal

    Hi, I have problems with the following: Number of modes for a 2d crystal with one atom per primittive unit cell. 1. Number of discrete vibrational modes? Should there be 2N of them? That is what I come up with if I think of one transverse and one longitudinal mode for each k. But I am...
  25. W

    Solving for degenerate oscillatory modes for three connected particles

    Homework Statement a) Write down the Lagrangian and show that the equations of motion are: m\ddot{θ_1}+k[2θ_1-θ_2-θ_3] = 0 m\ddot{θ_2}+k[2θ_2-θ_1-θ_3] = 0 m\ddot{θ_3}+k[2θ_3-θ_1-θ_2] = 0 b) Show that the mode in which θ_1 = θ_2 = θ_3 corresponds to constant total angular momentum...
  26. Spinnor

    B-mode plots, spherical harmonics?, fundamental modes?

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  27. T

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    I wrote it in another thread but it got lost in the middle of the other comments. So, here goes my doubt: In some places I am reading things like the following: For example here: http://motls.blogspot.com.ar/2014/03/bicep2-primordial-gravitational-waves.html#more Where in the whole...
  28. Greg Bernhardt

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  29. D

    MHB Modes observable and modes controllable

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  30. U

    Optics: Whispering gallery modes in large systems

    While reading about whispering gallery modes, I have learned that whispering gallery modes can be seen for "microscopic spheres or toruses" -Wikipedia- , But can they practically be observed in relatively large prisms or glass spheres (m or even cm magnitude) ?
  31. N

    Understanding Degenerate and Hybrid Modes in Rib Waveguide Structures

    Hi, I am looking into some simulations of rib waveguide structures using Finite Element Method. I particularly solving modes for a 2D cross section of the optical waveguide, looking at TE and TM modes. My questions is about modes called "degenerate" and "hybrid" modes. I haven't found...
  32. Y

    MATLAB Plotting normal modes in Matlab from data in Patran

    Hi, Could You help me with problem mentioned in the topic? I copied translational data (3 column vectors) from modal analysis in Patran (from f06 file). Now I have problem in reproducing the results in Matlab. I am trying to draw normal modes in Matlab, but I haven't got much luck so far...
  33. C

    Normal modes of oscillation

    Homework Statement So I'm given two horizontal masses coupled by two springs; on the left there is a wall, then a spring with k_{1}, then a mass, then a spring with k_{2}, and finally another mass, not attached to anything on the right. The masses are equal and move to the right with x_{1}...
  34. A

    Vibrational modes of a discrete particle string

    I just want to make sure I understand the normal modes of a vibrating system of particles with discrete spacing. I have tried to drawn what I understand as the lowest and highest frequency mode of the standing waves. Is the drawing correct? Edit: actually I have drawn the maximum frequency where...
  35. N

    Normal Modes of a Triangle Shaped Molecule

    Homework Statement A molecule consists of three identical atoms located at the vertices of a 45 degree right triangle. Each pair of atoms interacts by an effective spring potential, with all spring constants equal to k. Consider only planar motion of this molecule. What are 6 normal modes and...
  36. S

    Vibrational modes of quartz crystal

    I have a problem about the vibrational modes of a quarts crystal Two vibrational modes are induced simultaneously in a quartz crystal at MHz frequencies via a transducer hooked up to two signal generators it appears as if a third average frequency is also generated but only becomes...
  37. ajayguhan

    Understanding Normal Modes of Objects - Linear vs Non-Linear Particles

    What does one mean by normal mode of an object? Why is it 3n-5 for linear particles, 3n-6 for non linear particle where n is the number of particle.
  38. carllacan

    Finding normal modes of a 3D object

    Hi. I'd like to find the normal modes / harmonics, displayed in a dB - Hz graph, of a given 3D object, namely a wind instrument shaped like a hyperbolic con with holes. I'm trying to perform simulations on Comsol Multyphysics, but I don't know how to do it. Is Comsol the best suited software...
  39. Z

    Uncovering the Mystery: Higgs Decay Modes and the Weight Paradox

    Under the Higgs in wiki it says "Another possibility is for the Higgs to split into a pair of massive gauge bosons. The most likely possibility is for the Higgs to decay into a pair of W bosons (the light blue line in the plot), which happens about 23.1% of the time for a Higgs boson with a mass...
  40. S

    TE, TM and TEM Modes in Lasers

    Greetings everyone, I am confusing the definitions in the title of the post all the time. I have books about lasers, yet none of them explain these concepts lucidly and clearly in my opinion. For example, what is our reference plane when we are dealing with semiconductor laser diodes and...
  41. N

    Does amorphous solids support phonons or nomal modes of vibration.?

    Does amorphous solids support phonons or nomal modes of vibration.?? Can we apply the concept of phonons and Debye Model in case of amorphous and poly-crystalline solids?? http://en.wikipedia.org/wiki/Phonon http://en.wikipedia.org/wiki/Debye_model The links I have attached above...
  42. N

    Normal modes of a string thought experiment

    Hey! So If I have a stretched string of length L fastened at one end, and I am moving the other end sinusoidally, will a standing wave appear ONLY if I move the other end with one of the normal-mode frequencies of the string? If not, will the resulting wave be a moving wave which is a...
  43. O

    Equipartition Theorem and Number of Modes

    I was looking at this page: http://en.wikipedia.org/wiki/Molecular_vibration And saw that they have six different vibrational modes listed for the water molecule. Elsewhere on they page they discuss the "3N-6" rule for determining the number of vibrational modes of a polyatomic molecule...
  44. A

    What Are Acoustic Phonon Modes in Calculating Heat Capacity of a Solid?

    In calculating the heat capacity of a solid due to the phonons in the low temperature limit, I am given the impression that the idea is to calculate the amount of standing wave modes available for the phonons in the solid. Is this the correct idea? But then in calculating the Debye temperature...
  45. A

    Optical and acoustic modes

    Basically phonons in crystals can either be acoustic or optical according to my book. But then it stresses that a necessary condition for this to hold is that the crystal has more than atom per primitive basis. The optical modes are then when neighbouring atoms oscillate out of phase (i.e. no...
  46. H

    Solving paraxial equation (to get cavity modes)

    Hello, I've been going through some cavity material and attempted analyses regarding transverse modes. Invariably, they always deal with general solutions of paraxial equation and do not have solutions specific to specific cavities I do know that general solutions to paraxial equation...
  47. F

    CMB polarization: the E and B modes

    Hi all! In Ruth Durrer's book "The Cosmic Microwave Background" there is this picture (Fig. 5.2 page 193) about the E and B mode of the CMB polarization: http://imageshack.us/photo/my-images/11/s7o6.png/ http://imageshack.us/photo/my-images/11/s7o6.png/ They represent the E and B...
  48. M

    Are Muons and Tauons Higher-Dimensional KK Modes?

    Muons and tauons as KK modes?? Hello, everybody: I have (what I think is) a silly question. We all know that μ and τ particles are just as electrons, but with larger mass. Could it be that they are heavier Kaluza-Klein modes of the e in a higher dimensional theory, where the extra dimension...
  49. B

    Assumed modes and their units

    Hi, I am trying to understand the assumed-modes approach to solving vibration problems. For example, the transverse deformation of a cantilever beam is using two assumed modes is given as ζ(x,t) = ψ_{1}(x)q_{1}(t) + ψ_{2}(x)q_{2}(t) ψ_{1}(x) = (x/L)^{2}; ψ_{2}(x) = (x/L)^{3} In this...
  50. J

    Optical waveguide modes with different speed, what happens?

    Hi, I'm new on the forum and I would like to start with a question. I've searched for a reply in old posts with no success. If you can help me to find an answer I'll be very glad. Talking about optical modes inside a waveguide. If a waveguide support two different modes, say TM and TE mode...
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