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1

Christman, Brian W. "Standing Waves." Annals of Internal Medicine 172, no. 2 (January 21, 2020): 104. http://dx.doi.org/10.7326/m19-0937.

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2

Gogberashvili, Merab, Irakli Mantidze, Otari Sakhelashvili, and Tsotne Shengelia. "Standing waves braneworlds." International Journal of Modern Physics D 25, no. 07 (June 2016): 1630019. http://dx.doi.org/10.1142/s0218271816300196.

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The class of nonstationary braneworld models generated by the coupled gravitational and scalar fields is reviewed. The model represents a brane in a spacetime with single time and one large (infinite) and several small (compact) spacelike extra dimensions. In some particular cases the model has the solutions corresponding to the bulk gravi-scalar standing waves bounded by the brane. Pure gravitational localization mechanism of matter particles on the node of standing waves, where the brane is placed, is discussed. Cosmological applications of the model is also considered.
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3

Ouseph, P. J. "Standing longitudinal waves." American Journal of Physics 55, no. 7 (July 1987): 666–67. http://dx.doi.org/10.1119/1.15045.

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4

Wilkening, Jon. "Traveling-Standing Water Waves." Fluids 6, no. 5 (May 14, 2021): 187. http://dx.doi.org/10.3390/fluids6050187.

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We propose a new two-parameter family of hybrid traveling-standing (TS) water waves in infinite depth that evolve to a spatial translation of their initial condition at a later time. We use the square root of the energy as an amplitude parameter and introduce a traveling parameter that naturally interpolates between pure traveling waves moving in either direction and pure standing waves in one of four natural phase configurations. The problem is formulated as a two-point boundary value problem and a quasi-periodic torus representation is presented that exhibits TS-waves as nonlinear superpositions of counter-propagating traveling waves. We use an overdetermined shooting method to compute nearly 50,000 TS-wave solutions and explore their properties. Examples of waves that periodically form sharp crests with high curvature or dimpled crests with negative curvature are presented. We find that pure traveling waves maximize the magnitude of the horizontal momentum among TS-waves of a given energy. Numerical evidence suggests that the two-parameter family of TS-waves contains many gaps and disconnections where solutions with the given parameters do not exist. Some of these gaps are shown to persist to zero-amplitude in a fourth-order perturbation expansion of the solutions in powers of the amplitude parameter. Analytic formulas for the coefficients of this perturbation expansion are identified using Chebyshev interpolation of solutions computed in quadruple-precision.
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5

AUTHIER, A. "X-RAY STANDING WAVES." Le Journal de Physique Colloques 50, no. C7 (October 1989): C7–215—C7–224. http://dx.doi.org/10.1051/jphyscol:1989723.

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6

Becker, Janet M., and John W. Miles. "Standing radial cross-waves." Journal of Fluid Mechanics 222, no. -1 (January 1991): 471. http://dx.doi.org/10.1017/s0022112091001180.

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7

Leonovich, A. S., and V. A. Mazur. "Standing Alfvén waves with." Annales Geophysicae 16, no. 8 (1998): 900. http://dx.doi.org/10.1007/s005850050660.

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8

Deelman, J. C. "Standing waves in cementstone?" Materials and Structures 19, no. 5 (September 1986): 395–400. http://dx.doi.org/10.1007/bf02472130.

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9

Gíslason, Kjartan, Jørgen Fredsøe, Rolf Deigaard, and B. Mutlu Sumer. "Flow under standing waves." Coastal Engineering 56, no. 3 (March 2009): 341–62. http://dx.doi.org/10.1016/j.coastaleng.2008.11.001.

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10

Gislason, Kjartan, Jørgen Fredsøe, and B. Mutlu Sumer. "Flow under standing waves." Coastal Engineering 56, no. 3 (March 2009): 363–70. http://dx.doi.org/10.1016/j.coastaleng.2008.11.002.

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11

Morgenröther, K., and P. Werner. "Resonances and standing waves." Mathematical Methods in the Applied Sciences 9, no. 1 (1987): 105–26. http://dx.doi.org/10.1002/mma.1670090110.

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12

Carvalho, Paulo Simeão, and Marcelo Dumas Hahn. "Standing waves on holidays." Physics Education 58, no. 6 (October 11, 2023): 065027. http://dx.doi.org/10.1088/1361-6552/acfbd5.

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Abstract Standing waves are a common phenomenon in nature, but sometimes difficult to understand by the students. Many of them do not realise, for example, that the sound coming from the musical instruments is due to standing waves that are formed in strings, membranes, or cavities on those instruments. In this paper, we describe a simple activity that occurred in a circular pool during holidays which excited people for generating standing waves with their own body. This was also an opportunity for talking about this phenomenon with young people and make simple calculations of the speed of waves in shallow water. This is an example that summertime is not just for relaxing and teachers may find good examples of applied physics to bring to their classes and help students to better understand physics contents.
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13

Dostal, Jack A. "Longitudinal standing waves, mechanical waves, and diagnostics." Journal of the Acoustical Society of America 153, no. 3_supplement (March 1, 2023): A147. http://dx.doi.org/10.1121/10.0018458.

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The Standing Wave Diagnostic Test is a 22-item multiple choice survey designed to assess student understanding of longitudinal standing waves in air. I created it to measure my students’ difficulties with the subject. I also created the Longitudinal Standing Wave Tutorial to address these difficulties. The tutorial uses marked springs, tuning forks, pipes, and plenty of discussion to develop students’ understanding. Both the diagnostic and tutorial are based in physics education research and developed using survey and interview data from college physics classes. I often use the tutorial as a laboratory exercise in my Physics of Music class, which generates some interesting differences from the college physics classes. Some are a result of students’ prior knowledge about sound, while others are influenced by the course material covered prior to the tutorial. I will discuss some of my own results with these materials and put them in context with other physics education research based mechanical wave surveys.
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14

Miles, John. "Parametrically excited, standing cross-waves." Journal of Fluid Mechanics 186 (January 1988): 119–27. http://dx.doi.org/10.1017/s0022112088000060.

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Luke's (1967) variational formulation for surface waves is extended to incorporate the motion of a wavemaker and applied to the cross-wave problem. Whitham's average-Lagrangian method then is invoked to obtain the evolution equations for the slowly varying complex amplitude of the parametrically excited cross-wave that is associated with symmetric excitation of standing waves in a rectangular tank of width π/k, length l and depth d for which kl = O(1) and kd [Gt ] 1. These evolution equations are Hamiltonian and isomorphic to those for parametric excitation of surface waves in a cylinder that is subjected to a vertical oscillation, for which phase-plane trajectories, stability criteria and the effects of damping are known (Miles 1984a). The formulation and results differ from those of Garrett (1970) in consequence of his linearization of the boundary condition at the wavemaker and his neglect of self-interaction of the cross-waves in the free-surface conditions (although Garrett does incorporate self-interaction in his calculation of the equilibrium amplitude of the cross-waves). These differences have only a small effect on the criterion for the stability of plane waves, but the self-interaction is crucial for the determination of the stability of the cross-waves.
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15

Carandini, M., R. A. Frazor, and A. Benucci. "Standing waves and traveling waves in visual cortex." Journal of Vision 6, no. 13 (March 28, 2010): 25. http://dx.doi.org/10.1167/6.13.25.

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16

Bondi, Sir Hermann. "Gravitational waves in general relativity XVI. Standing waves." Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 460, no. 2042 (February 8, 2004): 463–70. http://dx.doi.org/10.1098/rspa.2003.1176.

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17

Bryant, Peter J., and Michael Stiassnie. "Water waves in a deep square basin." Journal of Fluid Mechanics 302 (November 10, 1995): 65–90. http://dx.doi.org/10.1017/s0022112095004010.

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The form and evolution of three-dimensional standing waves in deep water are calculated analytically from Zakharov's equation and computationally from the full nonlinear bounddary value problem. The water is contained in a basin with a square cross-cection, when three-dimensional properties to pairs of sides are the same. It is found that non-periodic standing waves commonly follow forms of cyclic recurrence over times. The two-dimensional Stokes type of periodic standing waves (dominated by the fundamental harmonic) are shown to be unstable to three dimensional disturbances, but over long times the waves return cyclically close to their initial state. In contrast, the three-dimensional Stokes type of periodic standing waves are found to be stabel to small disturbances. New two-dimensional periodic standing waves with amplitude maxima at other than the fundamental harmonic have been investigated recently (Bryant & Stiassnie 1994). The equivalent three-dimensional standing waves are described here. The new two-dimensional periodic standing waves, like the two-dimensional Stokes standing waves, are found to be unstable to three-dimensional disturbances, and to exhibit cyclic recurrence over long times. Only some of the new three-dimensional periodic standing waves are found to be stable to small disturbances.
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18

Glushchenko, A. G., E. P. Glushchenko, N. L. Kazanskiy, and L. V. Toporkova. "STANDING WAVES IN NONRECIPROCAL MEDIA." Computer Optics 37, no. 4 (January 1, 2013): 415–18. http://dx.doi.org/10.18287/0134-2452-2013-37-4-415-418.

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19

Sarafian, Haiduke. "Simulation of Transverse Standing Waves." World Journal of Mechanics 04, no. 08 (2014): 251–59. http://dx.doi.org/10.4236/wjm.2014.48026.

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20

Kamiński, Michał, Heiko Schulz-Ritter, and Martin Tolkiehn. "Magnetic X-ray standing waves." Acta Crystallographica Section A Foundations and Advances 77, a2 (August 14, 2021): C179. http://dx.doi.org/10.1107/s0108767321095039.

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21

Berry, M. V. "Superoscillations for monochromatic standing waves." Journal of Physics A: Mathematical and Theoretical 53, no. 22 (May 18, 2020): 225201. http://dx.doi.org/10.1088/1751-8121/ab8b3b.

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22

Abshagen, J., M. Heise, J. Langenberg, and G. Pfister. "Bifurcation behavior of standing waves." Journal of Physics: Conference Series 137 (November 1, 2008): 012005. http://dx.doi.org/10.1088/1742-6596/137/1/012005.

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23

Ruiz, Michael J. "Students dance longitudinal standing waves." Physics Education 52, no. 3 (March 30, 2017): 033006. http://dx.doi.org/10.1088/1361-6552/aa648e.

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24

Ferguson, Sarah Hargus. "Standing waves on piano wire." Journal of the Acoustical Society of America 129, no. 4 (April 2011): 2539. http://dx.doi.org/10.1121/1.3588437.

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25

Longuet-Higgins, Michael S. "Vertical jets from standing waves." Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 457, no. 2006 (February 8, 2001): 495–510. http://dx.doi.org/10.1098/rspa.2000.0678.

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26

Zegenhagen, Jörg. "X-ray standing waves imaging." Surface Science 554, no. 2-3 (April 2004): 77–79. http://dx.doi.org/10.1016/j.susc.2003.12.057.

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27

Williamson, Robert M. "Some standing waves aren’t quantized." Physics Teacher 34, no. 6 (September 1996): 326. http://dx.doi.org/10.1119/1.2344461.

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28

Mazuel, Lionel, and J. David Hardwick. "Standing waves at an outfall." Journal of Hydraulic Research 34, no. 2 (March 1996): 147–60. http://dx.doi.org/10.1080/00221689609498493.

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29

Miles, John. "Parametrically excited standing edge waves." Journal of Fluid Mechanics 214, no. -1 (May 1990): 43. http://dx.doi.org/10.1017/s0022112090000039.

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30

Iooss, Gérard, Pavel Plotnikov, and John Toland. "Standing waves on infinite depth." Comptes Rendus Mathematique 338, no. 5 (March 2004): 425–31. http://dx.doi.org/10.1016/j.crma.2004.01.002.

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31

Smith, Holly A., and Tara L. Tubbs. "Standing waves on a spring." Journal of the Acoustical Society of America 127, no. 3 (March 2010): 1913. http://dx.doi.org/10.1121/1.3384848.

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32

Alazard, Thomas, and Pietro Baldi. "Gravity Capillary Standing Water Waves." Archive for Rational Mechanics and Analysis 217, no. 3 (February 12, 2015): 741–830. http://dx.doi.org/10.1007/s00205-015-0842-5.

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33

Lee, Chang Jae. "Atomic de Broglie waves in multiple optical standing waves." Physical Review A 53, no. 6 (June 1, 1996): 4238–44. http://dx.doi.org/10.1103/physreva.53.4238.

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34

Bryant, Peter J., and Michael Stiassnie. "Different forms for nonlinear standing waves in deep water." Journal of Fluid Mechanics 272 (August 10, 1994): 135–56. http://dx.doi.org/10.1017/s0022112094004416.

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Multiple forms for standing waves in deep water periodic in both space and time are obtained analytically as solutions of Zakharov's equation and its modification, and investigated computationally as irrotational two-dimensional solutions of the full nonlinear boundary value problem. The different forms are based on weak nonlinear interactions between the fundamental harmonic and the resonating harmonics of 2, 3,…times the frequency and 4, 9,…respectively times the wavenumber. The new forms of standing waves have amplitudes with local maxima at the resonating harmonics, unlike the classical (Stokes) standing wave which is dominated by the fundamental harmonic. The stability of the new standing waves is investigated for small to moderate wave energies by numerical computation of their evolution, starting from the standing wave solution whose only initial disturbance is the numerical error. The instability of the Stokes standing wave to sideband disturbances is demonstrated first, by showing the evolution into cyclic recurrence that occurs when a set of nine equal Stokes standing waves is perturbed by a standing wave of a length equal to the total length of the nine waves. The cyclic recurrence is similar to that observed in the well-known linear instability and sideband modulation of Stokes progressive waves, and is also similar to that resulting from the evolution of the new standing waves in which the first and ninth harmonics are dominant. The new standing waves are only marginally unstable at small to moderate wave energies, with harmonics which remain near their initial amplitudes and phases for typically 100–1000 wave periods before evolving into slowly modulated oscillations or diverging.
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35

PENG, HUAIWU, and CUNBIAO LEE. "PERIODIC TRIPLING AND JET ERUPTION OF FORCED STEEP GRAVITY WAVES." Modern Physics Letters B 23, no. 03 (January 30, 2009): 397–400. http://dx.doi.org/10.1142/s0217984909018497.

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Period tripling of standing waves in a circular tank generated by the side-wall excitation is investigated for the first time. With the increasing of forcing acceleration after the appearance of axisymmetric standing wave, period-tripled non-breaking standing waves and violent jet eruption between the modes are observed. However, the physical mechanisms for the generation of the interesting period-tripled standing waves are still unknown and need further research.
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36

Sobey, R. J. "Analytical solutions for steep standing waves." Proceedings of the Institution of Civil Engineers - Engineering and Computational Mechanics 162, no. 4 (December 2009): 185–97. http://dx.doi.org/10.1680/eacm.2009.162.4.185.

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37

Pratt, David T., Joseph W. Humphrey, and Dennis E. Glenn. "Morphology of standing oblique detonation waves." Journal of Propulsion and Power 7, no. 5 (September 1991): 837–45. http://dx.doi.org/10.2514/3.23399.

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38

Babayan, Yelizaveta, Jeffrey M. McMahon, Shuzhou Li, Stephen K. Gray, George C. Schatz, and Teri W. Odom. "Confining Standing Waves in Optical Corrals." ACS Nano 3, no. 3 (February 25, 2009): 615–20. http://dx.doi.org/10.1021/nn8008596.

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39

Kalinichenko, V. A., and S. Ya Sekerzh-Zen’kovich. "Excitation of progressive-standing faraday waves." Doklady Physics 56, no. 6 (June 2011): 343–47. http://dx.doi.org/10.1134/s1028335811060024.

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40

Aksenov, V. L., V. K. Ignatovich, and Yu V. Nikitenko. "Neutron standing waves in layered systems." Crystallography Reports 51, no. 5 (October 2006): 734–53. http://dx.doi.org/10.1134/s1063774506050038.

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41

Gibbs, Robert E. "Standing waves on a hanging rope." Physics Teacher 36, no. 2 (February 1998): 108–10. http://dx.doi.org/10.1119/1.880006.

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42

Featonby, David, David Keenahan, and Marta Fernandez. "Standing waves in strings—the question." Physics Education 55, no. 5 (June 11, 2020): 057002. http://dx.doi.org/10.1088/1361-6552/ab5c01.

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43

Featonby, David, David Keenahan, and Marta Fernandez. "Standing waves in strings—the answer." Physics Education 55, no. 6 (August 13, 2020): 067001. http://dx.doi.org/10.1088/1361-6552/ab7445.

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44

Olum, Ken D., and J. J. Blanco-Pillado. "Radiation from Cosmic String Standing Waves." Physical Review Letters 84, no. 19 (May 8, 2000): 4288–91. http://dx.doi.org/10.1103/physrevlett.84.4288.

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45

Drakopoulos, M., J. Zegenhagen, A. Snigirev, and I. Snigireva. "Microscopy with X‐ray Standing Waves." Synchrotron Radiation News 17, no. 3 (May 2004): 37–42. http://dx.doi.org/10.1080/08940880408603093.

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46

Hernandez, G., R. W. Smith, J. M. Kelley, G. J. Fraser, and K. C. Clark. "Mesospheric standing waves near South Pole." Geophysical Research Letters 24, no. 16 (August 15, 1997): 1987–90. http://dx.doi.org/10.1029/97gl01999.

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47

An, T., K. Yamaguchi, K. Uchida, and E. Saitoh. "Thermal imaging of standing spin waves." Applied Physics Letters 103, no. 5 (July 29, 2013): 052410. http://dx.doi.org/10.1063/1.4816737.

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48

Maa, Dah‐You, and Ke Liu. "Nonlinear standing waves: Theory and experiments." Journal of the Acoustical Society of America 98, no. 5 (November 1995): 2753–63. http://dx.doi.org/10.1121/1.413241.

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49

Denardo, Bruce, Andrés Larraza, Seth Putterman, and Paul Roberts. "Nonlinear theory of localized standing waves." Physical Review Letters 69, no. 4 (July 27, 1992): 597–600. http://dx.doi.org/10.1103/physrevlett.69.597.

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50

Keeports, David. "Standing waves in a styrofoam cup." Physics Teacher 26, no. 7 (October 1988): 456–57. http://dx.doi.org/10.1119/1.2342574.

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