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# Wave Propagation - Science topic

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Is there a reasonable alternative to the theory of the expanding universe? I believe so -
The idea of an eternal universe is highly speculative and doesn't quite fit with our current understanding of the universe's origins, such as the Big Bang theory. Any idea that has been around for a century cannot be easily dismissed but the James Webb Space Telescope is casting potential doubts on the Big Bang. If this continues, we may well find ourselves in need of another theory explaining cosmic origins.
When we solve (19th-century Scottish physicist James Clerk) Maxwell's equations for light, we find not one but two solutions: a 'retarded' wave, which represents the standard motion of light from one point to another; but also an 'advanced' wave, where the light beam goes backward in time. ("Physics of the Impossible" by Michio Kaku, Penguin Books, p. 276-277) Einstein's equations say gravitational fields carry enough information about electromagnetism to allow Maxwell's equations to be restated in terms of these gravitational fields. This was discovered by the mathematical physicist George Yuri Rainich. (Electrodynamics in the general relativity theory. by G. Y. Rainich. Trans. Amer. Math. Soc. 27 (1925), 106-136 https://www.ams.org/journals/tran/1925-027-01/S0002-9947-1925-1501302-6/)
The farther away a star or galaxy is, the more the advanced part of waves from it will reach into the past, giving us a greater inaccuracy regarding its true distance. This increase is analogous to redshift increasing with distance. We might call it readshift - re(tarded) ad(vanced) shift. Readshift would explain the astronomical results which were interpreted as accelerating expansion of the universe. Surveyed supernovas would appear fainter, therefore apparently farther away than they truly are. Unless advanced waves are considered a possibility, the only rational way to move a supernova from its apparent, distant position to its true nearer location is to conclude the universe has expanded.
A backup to this point of view is presented in the article link at paragraph's end, in which a fresh perspective on the nature of electromagnetism is envisioned. The perspective uses John Wheeler’s geons and confines James Clerk Maxwell’s propagation of electromagnetic waves by oscillating electric and magnetic fields to a quantum-scale role. The confinement restricts the motion of photons – and via George Yuri Rainich, gravitons – to a “bobbing up and down” in the cosmic sea which is perpendicular to the direction of waves’ propagation. The severely limited movements of gravity (space-time) and electromagnetism mean the universe never expands or contracts. (8) (PDF) Measurement of Gravity Leads to Gravitons Decaying Topologically. Available from: https://www.researchgate.net/publication/375758112_Measurement_of_Gravity_Leads_to_Gravitons_Decaying_Topologically [accessed Nov 22 2023].
Surely an alternative to the Big Bang in which there’s no expansion or contraction (no oscillation in either space or time) must be an infinite, eternal cosmos. How is it even possible to think of creating something that has always existed? A model of the cosmos might be built that uses the infinite number pi and imaginary time, and resides in Virtual Reality (artificial, computer-generated simulation). The entanglement (quantum-mechanics style) in the simulated universe is unable to remain separate from the entanglement existing in our perceived reality because computers using so-called "imaginary time" (which is defined by numbers with the property i² = -1) remove all boundaries between the two universes. This enables them to become one Augmented Reality (known now as technology that layers computer-generated enhancements onto an existing reality but seen here as the related layering of virtual reality onto other points in time and space). The poorly named imaginary time of physics and mathematics unites with pi (both are necessary to generate a non-Big-Bang cosmos i.e. an infinite universe which, because space and time can never be separated, is eternal). This manipulation of time, space, and the universe with virtual and augmented reality might possibly be produced by the two-valued binary-digit system used in electronics traversing a wormhole, or shortcut between folds in space and time, designed by humans of the far future. The augmented reality which is layered on “other” points in space-time actually isn’t transmitted to other points. Because of the quantum entanglement of every particle (massive or massless) of everything in spacetime caused by advanced and retarded waves cancelling each other, only one point ever exists. Thus, transmissions to any (apparently other) places or times wouldn’t be restricted to the speed of light but can be made instantaneous by technology of the far future.
Christian sent me a message, asking me not to mention him again, so i won't expect an answer from him, however i find it convenient for a man of his "stature" to look down his nose at someone when else when they can't articulate what they are looking for. the question of Math is a matter of perspective, relative to the QuestionAnswer, else AnswerQuestion. in my case, i play devel's advocate where worst case is always presumed best case for reason cosmological. in terms of risk management, MyWay refers to Gas Vapor Dectection, which tells us more about metaphysics than theory, or Christain Science... just saying. the numbers involved include 72 216 1296 leading to 369 which isn't really speculation, it's TETRA #
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The theme of the diffraction typically refers to a small aperture or obstacle. Here I would like to share a video that I took a few days ago that shows diffraction can be produced by the macroscopic items similarly:
I hope you can explain this phenomenon with wave-particle duality or quantum mechanics. However, I can simply interpret it with my own idea of Inhomogeneously refracted space at:
When another finger is brought close enough, the semi-shadows from edges of that finger will overlap
In fact, similar and maybe even more pronounced effect can simply be observed by eye looking through a very narrow gap between two fingers. Bring two fingers very close (few cm) to one eye and look at distant uniform background e.g. sky or screen. By adjusting with the gap one may see some black strip or even a few of them arising. And at first look it may indeed look like diffraction.
However, one immediately realize that while light has almost 1:2 wavelength range so diffraction pattern would be colored and smeared if sourced by white or near white light.
Also, dimensions involved are much larger than needed to observe explicit diffraction.
The alternative explanations is overlaps of semi-shadows. E.g. the edge of better to say multiple ill-defined edges are de-focused by eye when finger is that close and that creates some grey semi-shadow around the edge/edges.
When another finger is brought close enough, the semi-shadows from edges of that finger will overlap creating some non-monotonic stripped patterns. That pattern looks similar to diffraction but in fact all defined by geometric optics ( actual distance, focus distance, aperture size).
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It is common that the polarization purity of EM wave will be deteriorated when the propagation environment is to be free space (with obstacles). So, is there any device to preserve the polarization purity of signal at least to a reasonable level (which is supposed to take its propagation in free space).
The polarisation of an em wave propagating in free space will be maintained. De-polarisation happens when the wave encounters a change in the free space environment. This could be a scattering object, for example a raindrop, or a change in the local propagation parameters due to changes in the atmosphere including the ionosphere. There is no single device that can stop this.
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The shadows of two objects undergo peculiar deformation when they intersect, regardless of the distance between the objects along the optical axis:
sorry, but such laser cexperiments have nothing to do with shadow blister effect.
In the shadow experiments, which are handling with bright white light from extended sources, one only deals with penumbras; diffraction effects cannot be seen due to the very low amount of diffracted light on a huge background.
In your diffraction related videos it is mentioned by yourself, that you have to (i) darken the lab for avoiding any backgroud signal and (ii) that you have to acquire the data over a lot of time...
Best regards
G.M.
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The fallacy of the aether was that its only function was to propagate light waves. This question goes much further and probes whether space (the vacuum) is an elastic medium that propagates waves at the speed of light. For example, do gravitational waves propagate in the elastic fabric of space? If space is assumed to be an elastic wave propagation medium, then gravitational wave equations imply this medium has enormous impedance of c3/G = 4 x 1035 kg/s.
This is a discussion question, and I am going to take the position that spacetime is an elastic medium with “spacetime foam” properties first proposed by John Wheeler. He determined that the uncertainty principle and vacuum zero-point energy implied space has Planck length oscillations at Planck frequency. This would make spacetime a physical medium that propagates waves at the speed of light with impedance of c3/G. This impedance is so enormous that a rotating wave with Planck length amplitude and an electron’s Compton radius would have an electron’s energy.
I am taking the position that the quantum vacuum is a sonic medium that propagates waves at the speed of light. This medium gives the vacuum its “intrinsic” properties such as vacuum permittivity εo, vacuum permeability μo, impedance of free space Zo, virtual particle formation, etc. If spacetime is not a physical medium, why does it have finite values for εo, μo and Zo? The following link has more information about my opinion and model. What is your opinion?
Of course, the proposed opus does not answer all the questions posed here. But I think it can be useful when looking for answers.
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We are currently investigating the shock response of materials using molecular dynamics (MD). This project showed us that the preparation of properly equilibrated MD models can be very challenging even for someone with a strong background in molecular modeling. Therefore, we thought of sharing some of our recent MD models with the research community. We would like to share the LAMMPS input and data files required to run MD simulations of shock wave propagation and ballistic impacts. I have provided ~3-minute video overview of the files here: https://youtu.be/hgZXvUdr-Qo
You can download the shock model from here: https://github.com/nuwan-d/MD_model_JAM-21-1174, and the impact model from here: https://github.com/nuwan-d/md_impact_tests
(Added on 2022/01/14): We recently published two more articles, and our MD (LAMMPS) and DFT (VASP) models are freely available.
The first is “Quantum and classical molecular dynamics simulations of shocked polyurea and polyurethane” (https://doi.org/10.1016/j.commatsci.2021.111166). The models are available here: https://github.com/nuwan-d/quantum_md_of_shocked_polymers
The second paper is “Molecular dynamics study on the shock induced spallation of polyethylene”( https://doi.org/10.1063/5.0072249). The models are available here: https://github.com/nuwan-d/shock_response_pe
(Added on 2022/06/08): Our latest MD (LAMMPS) and DFT (VASP) models of phase-separated polyurea are available here: https://github.com/nuwan-d/shock_response_of_polyurea
Good luck with your MD simulations.
I am not sure how that can be done in LAMMPS. Perhaps, this paper might give you some ideas:
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Dear all,
I am simulating the blast wave propagation inside a box (just opened in one of the 6 sides) using the coupling method LBE-MMALE. Detonation is loacted outside the box and in the direction of the open side. The box is considered to be rigid.
The entrance of the cubic box have an ambient layer, while all the other 5 faces of the air domain have clamped nodes (all DOFs are constrained). Is this a correct approach? Or should I implement any other BC's in the air domain in order to avoid the physical modelling of the box walls.
Rigid nodes is a conservative approach. It satisfied my needs at that time.
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Hi,
I am currently in my final year at university and for my dissertation I am investigating the propagation of flexural waves in a 2D structure with varying thickness. Currently, I am finding it difficult to find the reflection coefficient using COMSOL. At the moment I am modelling a uniform plate in a frequency domain with a range from 10 Hz to 10,000 kHz with an added excitation point from a point load, I am using a uniform plate so that I can validate a method of finding the reflection coefficient as it should be equal to 1 for a uniform plate.
I have attached the files for the uniform plate, if anybody has any ideas or solutions for my issue I would be hugely grateful.
Thank you
Hello!
This paper might be helpful for the reflection coefficient calculation
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Hi everybody.
I have developed within my research a 3 dimensional numerical wave tank (25 meter long, 10 meter wide and 6 meter water depth) in LS DYNA based on the ICFD method. I have already refined the mesh in the area where the wave acts to increase the accuracy of the wave deflection. At the outlet of the wave tank I have installed a numerical damper to minimize the reflection of the wave.
Now i have evaluated the results at 3 different locations (5m, 10m and 15m) and it is noticeable that energy is lost in the system. The wave deflection decreases at the results at 10m and 15m compared to the results at 5m. Reason for this could be numerical dissipation and numerical dispersion.
My idea now is to either increase the tank length to minimize the influence of the reflecting wave or to adjust the parameters of the linear and quadratic damping terms.
Does anyone of you know about similar problems and has some suggestions for me?
Thanks,
Jonas
Numerical dissipation and dispersion, as you say, mainly happens for two reasons: (i) insuffiecient number of cells per wave height/length (ii) inappropriate turbulence model.
I do not have any experience with ICFD within LS-DYNA but you should definitely test the results with more cells in the free surface area. Check the courant number not to exceed at least 0.3 in the FS area. Regarding turbulence models, the best but not ideal "out of the box" model for wave propagation is realizable k-E. If you wish that your simulations are long, then you will need different, more stabile turb. model.
All the best and good luck,
Ivan
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The results of our research determined for the first time that for the entire frequency range of acoustic waves, the range of their propagation, measured not in units of measurement of distance, but in cycles, is a constant: the same number of cycles corresponds to the same absorption of acoustic energy. But the presence of correlation in this case is not related to the presence of a cause-and-effect relationship between the frequency of acoustic waves and their propagation distance.
It should be noted that there are signs that the obtained regularity can be extended to transverse waves in water. This is evidenced by the fact that, unlike shorter wind waves, long ocean surface (transverse) waves of spread over a distance of more than 1000 km. Tsunami waves, which have a length greater than the length of "Zibu" waves, spread over a distance of tens of thousands of kilometers. Seismic waves that propagate in the solid shell of the Earth, at lengths close to the length of tsunami waves, also propagate for tens of thousands of kilometers. In the future, different types of waves propagating in different environments can be considered, which does not exclude the possibility of confirming the general (universal) physically justified and understandable regularity of wave attenuation put forward by us.
Dear Bernard Garnier. You do not agree with my postulate: "Long mechanical waves in all physical media propagate farther than short ones. This is a general law". The argument is very vague. It is necessary to give specific examples. Then there will be a subject for discussion. Based on your logic, the law of physics F=m*a and all other laws of physics are not universal? Sincerely, Boris Kapochkin.
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I modeled Lamb waves propagating in a carbon fiber composite plate by using the semi-analytic finite element method and solved the partial differential equation by using COMSOL PDE module. The Dispersion curve was consistent with that calculated by the "Dispersion Calculator". However, when I got the through thickness profiles obtained by the two methods, they were completely different. I don't know what is the cause of this problem?
For calculating the through-thickness profiles, the DC adopts the two conventions used by DISPERSE, as described in the DC (v2.2) manual, p. 11. The first is phase normalization. Since displacement, stress, and strain are complex, the phase of the second point (because the value at the first can be zero sometimes) from the top surface is taken, and the rest of the points is plotted with this phase, but only the real part. This is done for each component u1, u2, u3, sigma11, etc. Energy density and power flow density are integral quantities, so there is no phase to consider. The second convention is power normalization. All components are calculated for guided waves carrying a power of one Watt in the propagation direction x1, with the assumption that the waveguide is one meter wide. Then, when calculating the components at the same number of through-thickness points (samples x3, samples per layer) as DISPERSE, which uses 50 by default, you find very good agreement of the result from DISPERSE and from the DC.
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Conceptually, as well as source of wave propagation and wave equation
In an unbounded solid, there are two types of elastic waves: 1) dilatational (longitudinal waves), and 2) distortional (transverse waves); the distortional waves arise because solids can support shear, which true liquids and gases cannot support. In a bounded solid, the surface is subjected to Rayleigh waves (surface waves). Rayleigh waves are similar - but not identical - to gravity waves found at the surface of a bounded liquid.
[1] H. Kolsky; Stress Waves in Solids; Dover Publications, Inc.; 1963; pp. 4 & 16.
[2] Francis Weston Sears, Mark W. Zemansky; University Physics, Part 1 - Mechanics, Heat, and Sound; Addison-Wesley Publishing Company, Inc.; 1963; pp. 488-491.
Regards,
Tom Cuff
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How to calculate the amount of pressure generated by the ultrasonic transducer (single element or multi-phased transducer) after applying a certain voltage to it? I want to use this pressure field as the initial condition for longitudinal wave propagation simulation.
Knowing voltage is not enough. You must also know the frequency (or the shape of excitating pulse) and the impedance of transducer material and the surrounding medium. Additionally you must know, that no plate is vibrating in a way as a piston, but in a more complicated way.
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I want complete information about calibration methods of Network Analyzer. I want step-by-step calibration steps.
Is it better to measure waveguide components SOLT or TRL ??
What is the difference between SOLT and TRL?
See
I believe that equation 6 may be wrong and the signs in both top brackets should be negative.
You can generalise the equations to use any three different calibration loads (I think), but it is best if they are significantly different from each other.
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Hi,
I am working on numerical simulation of ultrasonic wave propagation through an elastic medium without any defect. I calculated the velocity of wave by using time and distance relationship. But when i used model with void or crack, i got less time to detect the first wave, while it should be longer as there is hole in model and wave propagation through it should be more. Can anyone help me out this problem i.e. how wave velocity is calculated in the model with defect.
I am trying to slove the standard rayleigh lamb frequency equation in isotropic plate using the newton Rapson method ( FORTRAN code ) but I am not able to capture all the root of the equation and modes, even not getting how to generate the data for plotting the dispersion curves... Kindly , please help.
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Hello to all
Two questions
1. Does the use of metals with high magnetic permeability, such as iron alloy in the waveguide, cause insertion losses?
2- What about chrome or copper plating?
If you know the article in this field, please introduce it. Thank you
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Dear all,
I want to apply the "periodic" boundary condition to the existing boundaries along wave propagation direction in a curved cell unit (attached image); However, this boundary condition does not appear to be applicable to curved surfaces, and some changes to the coordinate system used are required.
Unfortunately, I do not know what coordinate system to use and how to use it in "orientation of source".
I would be grateful if someone would help me.
Any help would be extremely appreciated.
Mehran Ebrahimi, I think you should add a new coordinate system, cylindrical one. In Definitions - Coordinate systems - Cykindrical system
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When we need to conduct a FE simulation of guided wave propagation, small element size and time step must be used to capture the waves, especially for high-frequency cases. Millions of elements would be normal for a model with a small size, say a plate with a dimension of 200mm*200mm*1mm. Is there any shortcut to avoid this type of difficulty or software that is more suitable for this work than ABAQUS or ANSYS, .etc?
Hi Han Lu
Whether/how much you can simplify this problem depends on many different factors. You may consider the following aspects:
- Is a two-dimensional model sufficient? -> Employ plane strain assumption.
- If not, can it be treated as axisymmetric? -> Exploit rotational symmetry in FEM or even solve (semi-)analytically
- Is the frequency very low? -> Use plate elements to avoid discretizing the thickness
- Is the frequency high? -> High-oder elements can be worthwhile, together with explicit solvers (if not frequency domain)
- Is the material linear? -> Solving in the frequency domain may be more effective.
- Is the structure of (piece-wise) constant cross-section? Semi-analytical approaches (SBFEM, TLM, SAFE) can be extremely efficient.
- Can the dimensions of the model be reduced by applying absorbing boundary conditions? -> Use SBFEM, PML, absorbing regions....
I hope this gives you some ideas to start. Feel free to ask about details of any of the approaches.
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Hello .
I want to design and build a waveguide load in X Band.
1- How to design that the VSWR is maximum 1.1? (What should I use inside the waveguide, what material? With what dimensions?)
2-How to test it with Network Analyzer after making it?
Buy a sheet of microwave absorber, cut a long triangle with a sharp point and glue it to one large wall of the waveguide with the point pointing towards where the power comes from, or glue two to both large walls. The longer the triangle and the sharper the point the better the match, generally. You can do it with stepped absorbers, or a pyramidal absorber too. It is hard to design to a vswr of 1.1 unless you design a stepped absorber and are very sure of its complex dielectric and magnetic constants, but making a taper longer will usually improve the vswr. The sharpness of the point is important. If it needs to cope with high power the sharpness of the point can be a problem because it may melt if the absorber has high absorption.
You could glue it to the side walls but it may need to be longer, depending whether the loss is magnetic or resistive.
You can also use a vane of nichrome on kapton film between slits on the centre-lines of the wide faces of the waveguide. If you do this you can adjust the way it tapers in while looking at the S11. https://www.dupont.com/products/kapton-rs.html might also be suitable.
You can test it on a Vector Network Analyser (VNA) with a good coax to waveguide adaptor. 1.1 vswr is about -26 dB so if you want to be reasonably accurate the adaptor needs to have S11 less than -40, unless you can calibrate on the waveguide side, using waveguide open short and load, for instance.
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I was wondering if surface electromagnetic waves can propagate at interface between two dielectrics, both isotropic and homogeneous, but having different relative permittivities.
The literature shows that their characteristics must be different.
Yes., there will be propagation of surface waves at the interface between the two dielectrics of the same properties. It is because they will have a different set of characteristics, which arise due to the difference in disturbance of equilibrium of positive and negative charges (Polarization). These displaced charges create an electric field of varying magnitude. It is different from the field produced by the surface wave.
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Consider a fluid-elastic structure interaction problem. We know that the density and shear module affect the elastic wave propagation velocity. Let's begin a discussion on the effect of density on the deformation intensity and recovering the shape.
The book entitled: Theory of Elasticity Vol. 7, 3rd Edition - 1984 by L D Landau, L. P. Pitaevskii, A. M. Kosevich, E.M. Lifshitz, Elsevier edition, covers some aspects of the thermal conduction & viscosity in solids from a hydrodynamic point of view. It covers for example how sound is absorbed in solids (with crystals symmetry) and a subtle topic, very very viscous fluids.
Best Regards.
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In an absorbing medium, the reflective index becomes a complex number: 𝑛̃ = 𝑛 ′ + 𝑖𝑛 ′′. Assume that a plane wave 𝐸⃗ (𝑥,𝑡) = 𝐸⃗ 0𝑒 −𝑖(𝜔𝑡−𝑘𝑥) is incident on this medium. (a) Starting from the plane wave dispersion in a medium (ω = 𝑐 𝑛 𝑘), show that the field intensity (|𝐸| 2 ) decreases exponentially over distance (i.e. |𝐸| 2 ∝ e −𝛼𝑥). (b) Express the absorption coefficient α in terms of other parameters.
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Hi
I wanna solve partial differential equation in terms of x and t (spatial and time), As I know one of the most useful way for solving pde is variable separation. well explained examples about mentioned way are wave equation, heat equation, diffusion....
wave equation is Utt=C^2 .Uxx
in other word; derivatives of displacement to time, equals to derivatives of displacement to spatial multiplied by constant or vice versa.
however my equation is not like that and derivatives are multiplied to each other.for example : Uxx=(1+Ux)*Utt
Im wondering how to solve this equation.
I will be thankful to hear any idea.
Dear Alireza Akbari looks like your equation is a nonlinear PDE, there are tables for those:
However I could not find yours, but don't worry, I tell you a trick we use in MHD.
1. You linearized it, i.e., you solve the PDE as a function of ei(k.r - omega t)
2. You get a complex polinom, but I don't see any parameters in your equation.
3. Anyway you can try an algebraic manipulator such as math or maple and find the roots. However, I find it strange that there is not a parameter, you need it to scan the complex solution.
Best Regards.
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I have heard that SWAN software is free software. But I am unclear whether SWAN software independtly exists or is it used in conjunction with Delft3d software.
Also, if there are any other software, please suggest.
That is a good question. I want to follow this.
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I want to apply a pulse-echo methodology (by using one single transducer as both transmitter and receiver). Do you know how to connect the transducer to the wave generator and oscilloscope to detect both transmitted pulse and echoes?
I have been trying to use the burst feature in manual mode by pressing the trigger button in the wave generator. However, when I do that, the oscilloscope is only capable of reading the wave generated instead of receiving as well the back-wall echo.
I am also using these types of transducers from Stemininc: Piezo Ceramic Plate 20x15x2.1mm 1 MHz, Piezo Ceramic Plate 7x7x0.2mm 250 KHz, and Piezo Ceramic Plate 20x15x3mm 710 KHz. Thus, I'm not sure if they are indicated to use this pulse-echo methodology.
I have two alligator cables connected to the oscillator and to the transducer: 1 to work as the transmitter and one to work as the receiver; and they are both connected in the same wires of the transducer. However, so far, it seems that these alligator cables connected to the same transducer are giving me the same wave.
Do you know if this equipment as it is is capable of doing these readings:
• reading of the transmitted and received waves (of amplitude vs. time), separately, by using this setup as is (when using two different cables), or
• reading of the transmitted and received waves combined in the same curve: maximum peak sent and resultant received echoes (back-end wall or cracks, for example)?
I am using a manually triggered pulse sine wave of amplitudes of either 10Vpp or 24Vpp, but the outcome is always identical. Should I be using a higher amplitude to make sure I receive the echoes?
Any help would be much appreciated.
You basically need a T/R (Transmit/Receive) switch between your signal generator and your transducer, and your oscilloscope and your transducer. When your signal generator is producing the outgoing periodic pulses used to drive your transducer, the T/R switch disconnects the oscilloscope from the transducer. While your transducer is receiving the reflected signal between the periodically generated pulses from the signal generator, the T/R switch connects the oscilloscope to the transducer, but disconnects the signal generator from the transducer. Note, be aware of the concept of range ambiguity, i.e., if the reflecting surface is further away than the round trip time between two of the signal generator's pulses, then the incoming reflected signal may fall between the next two pulses of the signal generator making the reflecting surface's distance appear shorter than it actually is.
How you actually realize your T/R switch will depend on your drive signal amplitude, and the input impedance of your oscilloscope.
Regards,
Tom Cuff
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Recently, I got a revision on one of my papers in which the reflection and transmission phenomenon of waves has been studied in a piezoelectric medium with the consideration of a flexoelectric effect.
In the said article I used the classical method for finding the amplitude ratios of the waves.
However, the reviewer suggests that
" It would have been better if the solution methodology was based on Lame displacement potentials where the dilatational and the distortional character of the waves are more easily distinguished."
But as far I know this methodology, the Lame potentials are best suited for the isotropic media.
So,
Is the Lame displacement potential method can be used for transversally isotropic media?
Dr. Sonal Nirwal in addition to the previous interesting answer, in Oil exploration seismic elastic wave propagation, the answer to your question is yes.
The Lame displacement potential method can be used for transversally isotropic media (VTI).
You can try to look at the following open access articles, which I found using Google search:
Best Regards.
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I want to establish the influence of prestress on the propagation characteristics of guided waves, and analyze which guided waves in which modes or frequencies are most sensitive to stress changes
Dear Li Jiaxin,
A good discussion of the foundations of initial stresses effect on guided waves can be found the literature, among them those published by Otmani et al.: https://doi.org/10.1016/j.compstruct.2020.112085
Generally, The fundamental guided modes can achieve superior of sensitivity to disturbances due to acoustoelastic effect, that could be considered for characterize the performance of the selected composite and structure.
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While going through different Rayleigh wave propagation papers. I have seen sometimes author is using Helmotz decomposition and sometimes not. What is rule? When should we use it? Any suggestions will be helpful.
Dear Dinesh, using HD reduces the model to simple system so that you would get the frequency equation. If would not use HD, you might be in trouble sometimes to get the frequency equation and related parameters of interest. If your model is simple one (for isotropic), then you can go in anyway. Hope you understand.
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Dear RG members:
Screenshot from:
Vonsovskii, S. V. and Svirskii, M. S. 1961. About the spin of phonons. Soviet Physics of the Solid State. 3:2160. In Russian.
Do you know any article/book which uses explicit expressions containing Anisotropic Elastic Langragians L( Cij )?
For instance: cubic, hexagonal, or tetragonal ones? Other symmetries are also welcome.
L can be written in the 4th index range - ijkl or Voig - ij notations, but the math expressions must contain explicitly the elastic stiffness components Cij or compliances Sij (if S-1 C ~ 1) according to the point symmetry group.
For example: in the isotropy case: 2, in the cubic case 3, in the hexagonal case 6 and so on.
A lagrangian is defined as L(Cij) = K( ρ v2 ) - U( Cij ), therefore the potential term U(Cij) does have to include an expression invariant to the point group symmetry considered.
I did an intensive search on the web, so far only two papers with two expressions (isotropic and cubic cases) both papers from the '60s.
Thank you all so much for the interest.
I have públished a preprint with the answer to this thread. The Lagrangian for D4 point group symmetry.
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Hello everyone,
I'm trying to implement a material with non-diagonal conductivity in my FDTD code. By the way, I'm using Dr. Elsherbeni's code for my purpose. Although I managed to implement diagonal anisotropy in my code, my code seems to be unstable for non-diagonal matrices. Through research, I've found out that my updating equations are not correct. Since it is necessary to interpolate the fields in irrelevant positions, it seems the updating equations also have to be organized differently than the isotropic case.
I attach the equations in a PDF below. the first equation on every page represents the equations in half-steps and the second one represents the updating equations implemented in the code.
Any help or hint would be appreciated.
I also have to point out that the source for the equations is the paper in the link below:
You are most welcome, Dear Amin Pishevar .
Best Regards.
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I am doing simulation in Abaqus. My topic is damage detection by using lamb wave propagation.
I am giving input data as sine sweep(48 sec). For that what is the time step and how much increment should use to get the output result and what is the approximate mesh size should be used. And what are the inputs we have to include in f-output and history output.
Feel free to get in touch with me for more explanation.
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I am currently modelling an acoustic planar wave, generated by a speaker, travelling through an expanding cross sectional area duct/horn system. When plotting a graph of transmission coefficient against frequency, the model suggests the transmission coefficient is between 0.5 and 1 for all frequencies. Should transmission coefficient, defined as the ratio of output to input amplitude, have a transmission coefficient above one, or do my results seem feasible?
Note, the medium through which the wave propagates is constant (air).
Sound is not water progressing in a pipe... You have to bring into your picture the notion of impedance matching between your sound source (the speaker membrane moved by a linear electromagnetic driver) and the medium (air in open field). The horn contributes to reduce the impedance gap hence increases the radiation effectiveness of the speaker - this is true only in a limited frequency band where the extent of the membrane is a fraction of the acoustic wavelength (every one knows you need bigger loudspeakers for lower frequencies). With a poor impedance matching only a mere fraction of the mechanical power will turn into acoustic power. This means that, for the same electro-mechanical driving force (or membrane velocity), you will increase the SPL in the open space by inserting your horn thanks to the better impedance matching, without contradicting the principle of energy conservation. This is what you have seen maybe - depending of the choice of "input" defining your global "transmission coefficient". As rightly commented by Anders, the impedance mismatch at any step of an "acoustic path" acts as a partial reflector: when the impedance matching is poor, the electromagnetic driver of the loudspeaker is unable to deliver "active power" in the open field. You can separate active and reactive power indirectly by measuring the out-phasing between tension and current in the coil (but you have to factor the Joule effect), or directly by measuring the sound intensity (e.g. from the pressure gradient https://en.wikipedia.org/wiki/Sound_intensity) anywhere along the acoustic path...
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Talking to Dr. Jörn Schliewe inspired me to raise this illustrated question and how you may call these barriers in the experiment of diffraction? Would you call it n-slits or n-obstacles?
Well, first, it’s N+1 obstacles or if you don’t want to count the long walls at either end for some reason, N-1obstacles, but certainly not N obstacles.
It certainly doesn’t matter what you call it. In your picture the two terms are both correct, and not mutually exclusive. It is in, in fact, N+1 obstacles forming N slits.
I don’t think anyone misunderstands that slits are formed by barriers, and if you talk about N slits everyone will instantly picture a barrier with slits in it. However, on a practical note, at optical wavelengths it generally isn’t possible to have free standing barriers like this. Instead the solid wall continues above and below. Generally a transmissive grating looks like a solid barrier with ”slits” cut into it. So the ”slits” term is constructivist. It is indicative of how the structure is created. You cut slits into a foil or similar. That is the dictionary definition of slit: a narrow cut. That is also how this became the standard terminology in optics because in the early experiments that is literally how gratings were made. We’ve greatly improved our “knife”, but fundamentally that is still how subtractive transmission gratings are still made today.
Terminology is for understanding, and often it uses similarity for recognition. No one thinks the arrow slits in a castle wall were literally made by cutting, but they look like cuts. If you call them slits everyone understands what you are talking about. That is the only important cr for terminology.
In optics we always talk about the slits. This is probably because we are focused on the light. Each slit is treated as a source, we propagate on using Huygen’s principle, etc. It doesn’t really matter what the barriers are so long as they exist. However, we have to talk about slit width and slit spacing, so in what an artist might call “negative space” we are inevitably also describing the barrier. Everyone gets that. I don’t think I’ll switch to explicitly talking about the barriers any time soon
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Staggered grid finite-difference (FD) methods are widely used for elastic wave equation modelling because of their high computational efficiency, smaller memory requirement and easy implementation. I am looking for the mathematical foundation for higher order (8th) of finite difference staggered-grid method on 2D P-SV elastic wave propagation.
Dear Dr.
Ijaz Durrani
,
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If water waves are disturbance of the water medium , the light is electromagnetic waves, and the gravity is space-time waves, then what is the medium in which the quantum waves propagate?
My guess Dr. Abdallah Barjas Qaswal is that there are not quantum waves the same way that there are not quantum fields.
Improper use of terminology, physics is no mathematics.
I have read famous advanced books for postgraduates in Physics in the past talking about "quantum fields", but nobody knows what a "quantum field" is.
Best Regards.
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I am using transient solution type in HFSSv15, and two same UWB Antennas are in far field of each other. One antenna is transmitting and other antenna is receiving antenna.
I don't think so , you have to use a Matlab script to calculate it
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I have read numerous research papers on various mechanisms of excitation of surface plasma wave. But why do we need to excite a wave? Is it necessary? Can't the wave propagate without being excited?
Interesting Prof. Moses Simon, surface plasmons are resonances of ElecMagWav and PlasWav in a metallic dielectric interface, they do exist experimentally only at low k vector waves.
I guess that excitation means the experimental procedure to get the same phase for both waves.
In that sense a Russian scientist. Prof. A. Pyatakov * defines plasmons as (I unquote him) as "a kind of "centaur": the upper part of which is an electromagnetic wave in a dielectric, and the lower part is a wave in an electron plasma formed by free electrons in a metal.
These two waves are in phase and travel at the same speed, which can be an order of magnitude less than the speed of light."
PersT ™ Volume 15 Issue 23 December 20, 2008.
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I need information concerning the penetration and reflection capacity of ultraviolet and infrared radiation wavelengths on different most common materials.
Edit.
Can somebody recommend a book to learn about? I'm especially interested in spectrogroscopy with a city environment materials and albedo.
First of all it depends to the material studied, and for me i guess that IR is more better then UV cause its wavelength is bigger than UV.
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Can someone provide the wave propagation assumption that applies to the transfer function-based square impedance tube method. How it differs from a cylindrical impedance tube?
Ijaz Durrani
Thanks Sir
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If we consider a marine communication scenario, what are the factors affecting the propagation of radio waves other than reflection, refraction, diffraction, scattering, and antenna height?
absorption
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As part of my research, I need to couple a loaded, custom-sized, rectangular, waveguide (in which a hybrid mode propagates at 8.5GHz) to either a) a coaxial transmission line or b) to a standard X-band waveguide.
I need to understand the design and optimization processes for both including impedance matching and/or mode conversion as required.
What is the best, most efficient way of approaching such a task?
Any useful resources on the topic would also be very much appreciated.
Kind Regards
Simon
ok I see ..some metamaterial..which definition for the "wave impedance" are you using.?.500 Ohm appears rather high to me and depends on the type of mode.For more detail you can consult the books by Pozar on microwave engineering
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Hi,
I am looking for a good summary of advances done in the field of multiscale modeling. Would appreciate it if people working in this domain could link me to relevant publications/ articles.
Thanks,
Pranoy Nair
I recommend the follow reviews on computational approaches of metal-organic-framework by Professor Coudert's group:
Fraux, G.; Chibani, S.; Coudert, F.-X., Modelling of framework materials at multiple scales: current practices and open questions. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 2019, 377 (2149), 20180220.
Evans, J. D.; Fraux, G.; Gaillac, R.; Kohen, D.; Trousselet, F.; Vanson, J.-M., et al., Computational Chemistry Methods for Nanoporous Materials. Chemistry of Materials 2016, 29 (1), 199-212.
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I wish to apply Floquet boundary condition at left-right ends and up-down ends, and the wish to find out the dispersion relation for the unit cell.
But I fail to find any option of Periodic condition in the list. If I make this an area-type geometry or a volume-type geometry, I can find the option, but not for the geometry provided (see attached image).
Floquet-Bloch periodic BC in COMSOL is applied on surfaces in 3D or edges/lines in 2D. This is because the source point is computed using a rotation of the position relative to the destination, i.e. rotation matrix R is computed. This is usually evaluated from the cross product of the source and destination boundary normal directions. Since normal directions are not defined for a point (which is exactly what you intend to select in your particular FE setup), the software does not provide that option.
The "Spadoni et al., Wave Motion, 40(7) (2009)" paper uses the discretized FE model approach by treating the rigidly connected lattice links as Timoshenko beams. In fact, the best way would be to model the 2D/3D geometry of the unit cells without making an assumption of rigid connectors/beam theories.
Check below the two papers that model periodic BCs of the auxetic unit cells, one uses the beam model approach while the other uses full geometry:
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To draw fragility surface based on the peak ground acceleration (PGA) and wave propagation velocity (PV), it is necessary to make accelerogram with different values ​​of the PGA and PV.
Is it possible to change the wave propagation velocity in earthquake accelerogram? Or can I produce accelerograms with different wave propagation velocity?
Thank's
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Hi, I am trying to create a computation model of acoustic plane wave propagation through multiple layers of fluid. What should be the appropriate boundary conditions in my fluid-fluid interface? Thank you.
The pressure and the normal components of the velocity have to be continuous across the boundaries. See for example in Fundamentals of Acoustics by Kinsler, Frey, Coppens, and Sanders Chapter 6.
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I have the following scenario.
In a marine environment, an object X moves below the surface of water from point A to point B. As it moves it displaces water around it which creates ripples (or increases detectable pressure levels) in the surroundings. We have sensors Si installed underwater at distance di with known geographic positions. I want to know the following.
1. How do we measure the intensity I of the ripples (generated by the object) at any sensor Si located di meters away from the object?
2. How do we measure the time required for the propagation of the ripple from its origin to sensor Si such that sensor Si can detect intensity I.
Thanks
Hi Tariq. It was a suggestion i have given. Hope it works.
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I am in a urgent need for material explaining the basics of wave propagation in soils. I came across lot of advanced material, which deals with specific conditions. Kindly suggest a good book or article about this.
Dear;
Kindly check:
Ground penetrating radar 2004 2 ed
Regards
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I am conducting a project where underground blasting effects are analysed on soil and structures above the soil. I've currently only have a very basic Abaqus model of a soil block with an implicit dynamic step. A time history amplitude was induced on this basic block model of soil. It shows the stress wave propagations. It has parameters for the Mohr-Coloumb plasticity. I am looking for books or any literature to further understand how the vibration of the blast will effect the soil layer, and possibly different layers of soil (rocks, clay, silty, soil etc). Any help or advice is appreciated!
ERT
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I did an experiment on a glass composite thin plate and generated Lamb wave. I increased the stiffness of the plate by forming a sandwich structure. I could find Ao mode with very attenuated amplitude but So is very diminishing. Confused, as per my understanding, I should get both modes frequencies even if the amplitude is small. But only Ao I could obtain its frequency but So not.
The dimensions of the thin plate, the configuration of shaker or input device, support and/or constraint of the specimen during testing, the location or distribution of area being measured for signal to test for Ao & So, as well as what transducer(s) or optical technique(s) is/are being used for those measurements, and what circuits and software are being used to condition and process the signal after acquisition.
The are many reasons that may be causing attenuation or lack of effective detection or isolation of the desired or expected signals, including that they actually may not be there at sufficient energy level for effective detection. Are you sure your estimated values for So of the increased-thickness sandwich plate are reasonable and don't actually predict the lower So values? Are you measuring 'lamb' waves on one skin of the sandwich only or of the entire plate (i.e. do you have transducers on both surfaces of the plate with careful and accurate reproduction of phase in both cases, and relative to one and other? Do you isolate or effectively filter frequency or wavelength anywhere in the process of your data collection, conditioning and/or post-acquisition processing? Are the 'lamb' waves on the skin or in the overall plate, what is the ratio of characteristic wavelength to plate thickness and how did this change by your structural alteration?).
Without knowing more of your setup, you experiment and your instrumentation, it is difficult or impossible to offer meaningful guidance.
In terms of a general vibration measurement problem, what signal are you expecting and why? Does the measured value represent something that seems impossible or not, it the result within or nearly within the expected range, and if not, is there something in the method or instrumentation or conditioning/processing that might explain any observed discrepancy? Hope this helps.... -TH
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I used the waveguide port to excite the momopole antenna and get appropriate results and now i want to alter the type of port to discrete port but I got different results with discrete the port.
Any one have experienc to help?
I am not familiar with CST, I work in HFSS. In HFSS if the port is inside radiation box instead of waveport, a lumped port I used
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Hello,
I am working on the finite element modeling of the ultrasound wave propagation. I want to check the wave transmission from water (impedance 1.5 *10^6 kg/(m^2.s)) to two different materials:
#1: Density=1050 kg/m^3 wave speed=2297.2 m/s acoustic impedance=2.41 (*10^6 kg/(m^2.s))
#2: Density=2000 kg/m^3 wave speed=1664.5 m/s acoustic impedance=3.33 (*10^6 kg/(m^2.s))
Based on my model, the reflection from water to material 1 is higher than 2. What is the reason for it? Material 2 has higher impedance, therefore should lead to higher reflection!
The wave speed in material 2 is really close to the wave speed in the water (1500 m/s). Does this cause less reflection at the boundary?
Thanks,
Hamed
Hi Abdolrasol,
What about the transmission amplitude, for the two cases?
How did you connect the Solid boundary to the water boundary?
At the boundary, if you have an option to choose the slave/master material, do not give water as the master material.
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Hello,
I am working on the lamb waves based on the semi-analytical finite element method (SAFEM) in the laminate structures.
When drawing dispersion curves, a number of additional curves are created in the system. I wanted to know what caused these curves to form and how can I eliminate them.
You can see the diagram in the attached files.
Hi,
I resolved similar issue by using Tangent delta (Tan D) parameter .
To calculate and plot the dispersion curves , the wave-number from SAFE need to thresholded by choosing the appropriate value of Tan D value.
Hope this helps!!
Regards,
Dileep
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I have submitted a paper in a journal where a primary radiator is surrounded by 36 periodic symmetrical structures similar to what is shown in the attached picture.
I have named it a metsurface patch antenna. The reviewer thinks it is it is a "CP patch antenna coupled with parasitic elements" NOT a metsurface patch antenna.
I want to know how we can differentiate between parasitic elements and metsurface?
It's about propagation: desired effects, versus undesired effects.
Do you agree?
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I am simulating wave propagation in a plate. In that process, I need to apply nodal displacement in the radial direction at the actuator position. I entered the wave excitation signal in the amplitude module. But when I am trying to select the displacement direction, I am not finding any option to apply radial displacement. I have attached the image of what I want to achieve. If anyone can help me out, I will be grateful.
You are welcome. Good Luck.
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I am trying to run a coupled model (HD and SW MIKE 21), for a one year period (8760 time steps; 3600 time step interval). However, after approx 200 time steps there is an Abnormal Run error, 'Blow-Up wave height too large'. What are some reasons that would cause this, and some solutions?
Ariel Mohan Aesthetics in cities are not merely a matter of taste, but something that is linked to culture and what is most noble in a community. It reflects a world of meaning about that space and the people who occupy it, in addition to maintaining order and a sense of transcendence. Urban aesthetics is a way to exalt this world of meaning and express the ideals and values of a people. It is not a question of preserving the traditional because it is old, but of preserving the past due to its importance and beauty. Beauty is a spiritual good and, as a spiritual good, it is part of who we are. I recommend reading the attached text.
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I want to model 2D wave propagation in a different medium and its reflex from the boundary with different shapes like rectangular or circle. Is any software or Matlab script that can do this?
thanks a lot for your helping
Dear Rasul Shamohamadi , you can check the following site:
A finite-difference time-domain code for 2D modeling of acoustic wave propagation. FWM2DA
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Hello! I apologize for the long question, but I’m a bit lost so I’ll try to be as precise as I can.
I am trying to implement a time-domain PML formulation for wave propagation, which can be found in this work
Here, the author has developed a set of equations to deal with the wave propagation in fluid and solid medium (please refer to eq. 5.9 of the work as I can't copy-paste them here). They are valid throughout the whole domain (PML and the physical domain), and within the physical domain the equations simplify to the general wave equation.
I'm using FEniCS as the Finite Element solver, and I need to provide the weak form of the PDE I'm willing to solve. Fortunately the weak form is in the work too (please see eqs. 5.10a-d).
I'm concerned only with the wave propagation in the fluid region, so I consider only eqs. 5.10a and 5.10c. Moreover, in eq. 5.10a, I believe the term with the integral over gamma vanishes as there is no fluid-solid interface.
The problem is I need to provide the Weak Form in only one equation. I'm confused with the term d phi/dxj and I'm not sure how to rewrite eqs. 5.10a and 5.10c in the form a=L.
Can someone help me with this?
Many thanks!
Well, I have some experience with FEniCS. I think my question could be summarized into "how to write a linear system AX = b or a variational form a==L or F==0 out of this system of two equations?"
I think it is possible to rewrite the equations in a coordinate free form, this can help. But still, as far as I know, I have to put them all together to solve this using FEniCS.
Is it possible?
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I established a simple model in ABAQUS to simulate the stress wave propagating in a plane.
I set up the Infinite element CINPE4 on the border of the plane in .inp file. it more or less had some effects, but the boundary reflected wave can not be completely absorbed on the boundary.
Does anyone have the similar problem? How to deal with it? Thank you!
dear Dr. wang, did resolved your problem ? Which infinite or semi-infinite elements did you choose?
follow
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Dear all. Sensors are often used to detect specific physical phenomena (displacement, magnetic fields, temperature, etc.). The acquired signal is generally in the form current, voltage, etc. The signal waveform reflects the physical behavior of the phenomena to be inspected, but in no case the physical phenomena. Does the particle wave duality represent two ways of observing particle behavior ? Thank you for your comments.
We know light as a wave but when it interacts with matter, it exhibits particle properties (Photoelectric effect and Compton scattering) and we know electrons as particles but they exhibit the wave properties of interference and diffraction. They are carriers of momentum and energy and have both particle and wave characteristics!
You must know that, macroscopic objects such as electrons, display wave behavior but the corresponding wavelengths are too small to detect. At the microscopic level, the waves associated with material particles are of the same size or exceed the size of the system, so, microscopic particles exhibit clearly discernible wave-like aspects. The general rule is: whenever the de Broglie wavelength of an object is in the range of or exceeds its size, the wave nature of the object is detectable but if its de Broglie wavelength is much too small compared to its size, the wave behavior of this object is undetectable.
In classical physics, particles and waves are mutually exclusive and they exhibit different behaviors but Photons, electrons, and any other microscopic particles behave unlike classical particles and unlike classical waves. The theory of quantum mechanics can simultaneously make statements about the particle behavior and the wave behavior of microscopic systems. The true reality of a quantum system is that it is neither a pure particle nor a pure wave. Depending on the type of equipment used to detect, particles have the capacity to display either “particle” or "wave" features. For example, based on the double-slit experiment (that's amazing and you must read more about it), if we wanted to look at the particle aspect of the electron, we would need only to block one slit or leave both slits open but used an observational tool, but if we were interested only in its wave features, we would have to leave both slits open and don't used observational tools. This means that both the “particle” and “wave” features are embedded into the electron (all of the materials), and by modifying the detect tools, we can suppress one aspect of the electron (As a fundamental particle of the whole universe) and keep the other. When we subject an electron to Compton scattering, we observe only its particle aspects, but when we involve it in a diffraction experiment (double-slit experiment), we observe its wave behavior only. So if we measure the particle properties of a quantum system, this will destroy its wave properties and vice versa. Any measurement gives either one property or the other, but never both at once. We can get either the wave property or the particle but not both of them together!!!!
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We are all familiar with the presentation of the light-ray as a sequence of photons/energy-packets just like the figure shown.
What is the relation among "wave-length λ", the length between the black lines (name?), and the length between the red lines (name?) in the figure shown?
Does the overall amplitude (of black modes or red modes) have any relation to the amplitude of the sinoid-wave of monochromatic light?
4/5/2020
From capture I see the 2 black marks pointing a whole wave package, isn´t it?
From [1] we can read that, I quote:
• "... a wave packet (or wave train) is a short "burst" or "envelope" of localized wave action that travels as a unit..."
• "...a wave packet can be analyzed into, or can be synthesized from, an infinite set of component sinusoidal waves of different wavenumbers, with phases and amplitudes such that they interfere constructively only over a small region of space, and destructively elsewhere..."
So the aswer is yes, it has a direct relation with the amplitude of the sinoid-wave of monochromatic light. The A(k) in wikipedia reference [1] and the u ( x, t ) in "basic behaviors part" description, these 2 equations relate the wave packet to a sinoid-wave. In addition, I can recommend a very good book on these questions: the Berkeley Physics Course Vol 3, Waves [2]:
[2] Waves (Berkeley Physics Course, Vol. 3) by Frank S. Crawford Jr.
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Tools in Matlab for modelling ultrasonic wave propagation in composite material
Dear Elango,
Hope you are well!
One important point is to consider is the acoustical properties of the material, they must be known. After that you can use acoustic wave equations to describe the sound propagation in a material. The material parameters are> The material density roh and the modulus of bulk elasticity for gas mediums C.
Then the speed of the acoustic wave propagation c = sqr C/roh.
Best wishes
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Hello everyone!
I wonder way EM wave propagates in vacuum space unlike sound waves. As we know EM waves are generated by charges in motion. Similar question for Light propagation from the distant stars to earth. Is there any alternative physical interpretation of propagation phenomena ?
The propagation velocity of EM waves depends on quality of wave guide and thier physical properties (for example, it depends on the permeability and permitivity of medium, etc.) and less than light C velocity. This may be mean that EM magnetic propagation need to "medium" to propagate" with physical properties. In the other hand, some cosmic particles have speed more than light speed.
v = 1/ sqrt (epsilon_0 mu_0 ) with these 2 (permitivity & permitivity)values being the physical properties of the vacuum, but there is not a set of equations where these 2 constants are not given, your capture WaveFunction.png shows then inside of the couple field equations.
For an electromagnetic wave in vacuum, group velocity is equal to phase velocity, but in other media rather than vacuum, light speed is not universal & in addition electric fields exists in metalic surfaces, inside metals Eins is zero.
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In a structural dynamic wave propagation problem, is the displacement at a point a continuous function of time or is it a continuous function of time only after the wave reaches the point?
Hi Mir Aamir Abbas
I believe that it depends a bit.
For unbounded systems, there would not be much of a response before the wave reaches the receiver position. More on this below.
For bounded systems, one must cater for rigid body modes. These have infinite (or a very high) wave speed.
This may at first sound strange, but once we think about it a little, it becomes obvious (or there could simply not be any wave propagation on planet earth which has a high velocity indeed when viewed from the galaxy centrum).
To exemplify, in the case or airbag firing inside cars, there is a pressure increase at the driver's ear before the acoustic wave reaches it. This took the industry about 20 years to figure out and it can be correctly detected when using both pressure transducers and microphones. The former tracks Line Pressure and Sound, while the microphone only tracks sound.
So, for an unbounded system, the 'rigid body' response would still be there, but it would very low and thus something that can be ignored.
Now, let us complicate matters a bit. There is an amplitude dependent portion in wave propagation that causes the wave front to distort - it is referred to as steepening. Simply put, waves with a high amplitude travel faster than the linear free wave speed. After a distance, the peak catches up with the trough and the wave collapses and the process starts anew.
So, when %LP = 100*Pulsation/LinePressure = 100*Sound/Ambient is high, things may happen faster than we would otherwise expect. This is generally the case whenever LP is low, e.g. in vacuum systems, on the suction side of machines and so on.
More on the differences of pressure and steepening is found here. https://qringtech.com/2010/09/15/wave-steepening-increase-peak-pressure-piping-pumps/
I am sure one can compound the issue further if one would want to do so.
Just my 2 cents
Claes
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Hi guys,
I hope you are in the best of your health.
I am working on Lamb wave propagation in anisotropic composite laminates. I want to apply the non-reflection boundary conditions in the simulation model. I am expecting to avoid the reflections from the plate edge by using non-reflection edges. Any idea how it can be done in ABAQUS? Or any other way to avoid these unwanted reflections?
Thank you!
Saqib
Hi Saqib Hameed,
to remove reflections in transient simulations of Lamb waves, you can use an area with exponentially increasing damping. I modified the approach from Liu and Jerry
and used it successfully with CFRP structures. Unfortunately, my results are only published in German, but you can find equations, parameters and figures in section 4.2.5 of my thesis:
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I know that for isotropic materials, a rule for the maximum element size L_max is:
L_max < lambda_min / 10
where lambda_min is the min. wavelength, defined as:
lambda_min = c_T / f
where f is the excitation frequency and c_T the transverse wave speed:
c_T = sqrt(G/rho)
Now I wonder:
- Can I take the same approach for an orthotropic material?
- If so, how can I calculate or obtain the transverse wave speed?
In general it is possible to formulate the Christoffel equation for any given elasticity tensor assuming plane wave motion. This allows you to assemble the Christoffel matrix Gamma with
Gammaij = rho * Cijkl * dk * dl
for a particular (unit) direction vector d = {d1 d2 d3} (in which the assumed plane wave is moving) and with elasticity tensor C.
This in turn allows you to compute the quasi long wave speed and quasi shear wave speeds in any given direction as the eigenvalues of Gamma.
Consequently, you can find the minimum wave speed in all directions, which, in theory, should be allowed to be plucked in as a "substitute" to cT.
Indeed, the minimum wave speed for an isotropic elasticity tensor converges exactly to sqrt(G/rho). In case of weak transverse isotropy, it converges to sqrt(Gmin/rho). I have observed relevant effects on the minimum wave speed especially in cases of strong orthotropy or anisotropy.
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How can one define a Plane Wave?
If its intensity is constant and independent of the distance from the source in the far field, the locus of same intensity points can be traced to any shape, right? Then, why plane wave alone?
Agree with Prof. Victor V. Krylov answer, F(x,t) = F(x.n - ct) is a plane wave but
F(r,t) = 1 /r . F(r.n - ct) is not since in the latter case the source is needed. In addition, plane waves are infinite parallel planes normal to the phase velocity vector.
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Hello i attached system of wave equation which is solved by using FDM. But i could not run this in matlab program as like wave propagation.
So i need your help can any one help me to write a code of that Scheme which i attached.
Dear Md. Roknujjaman Ripon to be more specific, you need to show what method will you use to solve it, I see you have frecuency---omega finite difference equation, am I right? so what is the diferential equation you are trying to solve?
For example FDTD method is a nice one, it allows quite a lot of interesting features. For example use staggered grids to store different physical quatities and PML conditions to absorb at the borders domains.
also:
• asked a question related to Wave Propagation
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