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Effect of excitation frequency on pattern morphology using the medium cell (diameter = 24.25 mm) increasing from 50 Hz to 199 Hz in 1 Hz increments (10 Hz per row). The fold symmetry of each pattern (2fold, 4-fold, etc.) is reported beneath each panel. Rows 1, 2, and 3 are three replicates performed on different days.
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The standing wave patterns formed on the surface of a vertically oscillated fluid enclosed by a container have long been a subject of fascination, and are known as Faraday waves. In circular containers, stable, radially symmetrical Faraday wave-patterns are resonant phenomena, and occur at the vibrational modes where whole numbers of waves fit exac...
Citations
... Cymatics is the study of the visual effects produced by sound and vibration [30], an important tool in understanding resonance phenomena. Concerning the effect in fluids, a complete study reported by Sheldrake [31] presents the main experimental factors with the greatest influence on the formation of patterns for frequencies between 50 and 200 Hz. ...
Research into particulate polymer composites is of significant interest due to their potential for enhancing material properties, such as strength, thermal stability, and conductivity while maintaining low weight and cost. Among the various techniques for preparing particle-based composites, ultrasonic wave stimulation is one of the principal laboratory-scale methods for enhancing the dispersion of the discontinuous phase. Nevertheless, there is a scarcity of empirical evidence to substantiate the impact of stimulating materials with natural sound frequencies within the acoustic spectrum, ranging from 20 Hz to 20 kHz, during their formation process. The present work investigates the effect of acoustic stimuli with frequencies of 56, 111, and 180 Hz on the properties of an acrylic-based polymer and its discontinuous carbon-based composites. The results indicated that the stimulus frequency affects the cure time of the studied systems, with a notable reduction of 31% and 21% in the cure times of the neat polymer and carbon-nanofiber-based composites, respectively, after applying a frequency of 180 Hz. Additionally, the higher stimulation frequencies reduced porosity in the samples, increased the degree of dispersion of the discontinuous phase, and altered the composite materials’ thermal, optical, and electrical behavior.
... Matter excited by sound frequencies can be visualized by the morphology of vibrational patterns in the form of symmetrical geometries. Te patterns are known to be determined primarily by frequency, amplitude, and boundary condition of the observed medium [25]. Faraday waves were indicated to diagnose and diferentiate cancer cells from healthy cells in brain tissues, healthy cells demonstrated to generate symmetrical patterns while cancerous cells were more prone to generate nonsymmetric, chaotic patterns [26]. ...
... New observations on Faraday waves patterns morphology following sound excitation conducted on the Cymascope instrument, suggest that sound is holographic by nature [105]. Importantly, observations on Faraday waves pattern morphology following sound excitation are in agreement with observations on pattern morphology following mechanical excitation [106][107][108], both demonstrating that patterns are crucially afected by the excitation frequency and boundary condition of the observed medium [25]. Accordingly, in many frequency-based physiological interventions, varied and distinct efects are reported following excitation by specifc frequencies. ...
This study introduces Geometric Sound as a subfield of spatial sound featuring audio stimuli which are sonic holograms of mathematically defined 3D shapes. The effects of Geometric Sound on human physiology were investigated through EEG, heart rate, blood pressure, and a combination of questionnaires monitoring 50 healthy participants in two separate experiments. The impact of Geometric Sound on Faraday wave pattern morphology was further studied. The shapes examined, pyramid, cube, and sphere, exhibited varying significant effects on autonomic nervous system markers, brainwave power amplitude, topology, and connectivity patterns, in comparison to both the control (traditional stereo), and recorded baseline where no sound was presented. Brain activity in the Alpha band exhibited the most significant results, additional noteworthy results were observed across analysis paradigms in all frequency bands. Geometric Sound was found to significantly reduce heart rate and blood pressure and enhance relaxation and general well-being. Changes in EEG, heart rate, and blood pressure were primarily shape-dependent, and to a lesser extent sex-dependent. Pyramid Geometric Sound yielded the most significant results in most analysis paradigms. Faraday Waves patterns morphology analysis indicated that identical frequencies result in patterns that correlate with the excitation Geometric Sound shape. We suggest that Geometric Sound shows promise as a noninvasive therapeutic approach for physical and psychological conditions, stress-related disorders, depression, anxiety, and neurotrauma. Further research is warranted to elucidate underlying mechanisms and expand its applications.
... The patterns generated on these plates are called Chladni figures. Applying the same logic on different materials, different Chladni figures are formed [1,2]. The Chladni plate is a flat plate, fixed at the center, while being able to vibrate freely when excited externally. ...
Mode shapes and natural frequencies of mechanical structures can be determined with the Chladni approach. Visual patterns are generated on the Chladni plate if it is exposed to vibrations. These patterns are known as Chladni patterns/figures. Mechanical vibrators are used to excite the plates at particular frequencies for pattern generation, but based on the making and application, their range is limited up to 10 kHz. Piezoelectric transducers are a special kind of transducers that are capable of generating ultrasonic frequencies and if are attached to a plate, intricate visual patterns can be generated, based on the material properties and the shape of the plate. The current research focuses on experimenting with and simulating Chladni figures in the ultrasonic frequency range. The simulations were performed in ANSYS Workbench as a validation of the experimental work.
... For example, as noted by Liu [3]: measuring the surface tension of soft materials [4]; developing new photonic devices [5,6]; metamaterials [7,8]; applications in cell culture patterns [9,10]; detecting physiological processes of organisms [11]; monitoring earthworms [12]; modifying soil structure to increase crop yields [13][14][15]; medical ultrasound and photoacoustic imaging modalities [16]; Brillouin Light Scattering spectroscopy [17]; laser vibrometry [18]; and the development of new methods for eradicating viruses and bacteria [19][20][21]. Furthermore, as noted by Sheldrake [22], the behaviour of the observed resonant phenomena offers a model for analogous behaviour observed in both physical systems, e.g., [23][24][25][26], and biological systems, e.g., [27][28][29][30]. ...
... The occurrence of pattern formation, as well as pattern morphology, has been shown to be dependent on both internal factors such as the shape and size of the container [22,[46][47][48]; the properties of the fluid such as purity [49,50]; viscosity [51,52]; and the fluid volume [22,53], as well as external factors such as the driving frequency [22,46,54,55]; amplitude [22,46,[54][55][56]; temperature [45]; and even the topography of the bottom of the container [57]. ...
... The occurrence of pattern formation, as well as pattern morphology, has been shown to be dependent on both internal factors such as the shape and size of the container [22,[46][47][48]; the properties of the fluid such as purity [49,50]; viscosity [51,52]; and the fluid volume [22,53], as well as external factors such as the driving frequency [22,46,54,55]; amplitude [22,46,[54][55][56]; temperature [45]; and even the topography of the bottom of the container [57]. ...
Standing waves formed on a vibrating fluid layer when a critical amplitude is applied are known as Faraday waves. The morphology of the observed phenomena is dependent on both the frequency of vibration and the boundary conditions. To understand the degree of this dependency, as well as any internal or external factors, we investigated the resonant phenomena observed in a circular cuvette for a range of frequencies. We find the symmetry fold is dependent on both the driving frequency and the amplitude. However, variance was consistently observed which showed no significant dependence on internal or external factors. We discuss possible causes for this variance and potential future research.
... The antinodes therefore exist as either bright or dark parts of a CymaGlyph and the nodal points are the transition, or equilibrium, points where the light is reflected perpendicular to the light source (for example see Fig 1 and 7). Previous observations concluded that pattern formation is primarily determined by the excitation frequency [10], the boundary condition of the observed medium [10] and the viscosity of the excited liquid in the cell [8,9,11,12]. Interestingly, preliminary investigations suggest that the spatial characteristics of sound could also affect pattern morphology [13]. ...
... The antinodes therefore exist as either bright or dark parts of a CymaGlyph and the nodal points are the transition, or equilibrium, points where the light is reflected perpendicular to the light source (for example see Fig 1 and 7). Previous observations concluded that pattern formation is primarily determined by the excitation frequency [10], the boundary condition of the observed medium [10] and the viscosity of the excited liquid in the cell [8,9,11,12]. Interestingly, preliminary investigations suggest that the spatial characteristics of sound could also affect pattern morphology [13]. ...
... The time for a pattern to fully form, which can be observed by the naked eye and which can be more quantitatively determined from the grey pixel count [10] (e.g. see Video 1A-B). ...
Nonlinear standing waves known as Faraday waves are formed in vibrating liquids enclosed by a container. In an effort to further our understanding of the relation between frequency and wave propagation within spatial boundaries we present a taxonomy to classify the variety of the observed resonant phenomena. This taxonomy includes some new definitions and suggests a unified language for describing wave propagation phenomena. We investigated the observed resonant phenomena and complex nonlinear dynamics utilising the Cymascope instrument, which works by transposing sound periodicities to water molecule periodicities.
... For example, Faraday instability can be used to make measurement equipment or measure material parameters, such as measuring the surface tension of soft materials [7], developing new photonic devices [8,9], metamaterials [10,11], etc. In addition, it has potential applications in biology [12] and medicine, such as application in cell culture patterns [13,14] and detecting physiological processes of organisms [15]. It can also be used to monitor and control animal behavior such as earthworms [16], sense and modify soil structure as well as to increase crop yields [17][18][19], medical examinations of medical ultrasound and photoacoustic imaging modalities [20], Brillouin Light Scattering spectroscopy [21], laser vibrometry [22] and develop new methods of eradicating viruses and bacteria [23][24][25]. ...
... By substituting Equation (9) of the stress tensor into Equation (12), the expression for the normal pressure at free surface is obtained, ...
Faraday instability has great application value in the fields of controlling polymer processing, micromolding colloidal lattices on structured suspensions, organizing particle layers, and conducting cell culture. To regulate Faraday instability, in this article, we attempt to introduce an elastic polymer film covering the surface of a viscous fluid layer and theoretically study the behaviors of the Faraday instability phenomenon and the effect of the elastic polymer film. Based on hydrodynamic theory, the Floquet theory is utilized to formulate its stability criterion, and the critical acceleration amplitude and critical wave number are calculated numerically. The results show that the critical acceleration amplitude for Faraday instability increases with three increasing bending stiffness of the elastic polymer film, and the critical wave number decreases with increasing bending stiffness. In addition, surface tension and viscosity also have important effects on the critical acceleration amplitude and critical wave number. The strategy of controlling Faraday instability by covering an elastic polymer film proposed in this paper has great application potential in new photonic devices, metamaterials, alternative energy, biology, and other fields.
... When the wavelength is not sufficiently small compared to the lateral boundaries, Faraday waves interact with these boundaries, which affects the final pattern. Circular containers, for example, can be used to produce patterns with n-fold rotational symmetry [39,146], while (small) square or rectangular containers promote different modes and dynamics [110,152] consistent with that geometry. ...
We give a brief review of several prominent fluid instabilities representing transitions driven by gravity, surface tension, thermal energy, and applied motion/acceleration. Strategies for controlling these instabilities, including their pattern formation properties, are discussed. The importance of gravity for many common fluid instabilities is emphasized and used to understand the sometimes dramatically different behavior of fluids in microgravity environments. This is illustrated in greater detail, using recent results, for the case of the frozen wave instability, which leads to large columnar structures in the absence of gravity. The development of these highly nonlinear states is often complex, but can be manipulated through an appropriate choice of forcing amplitude, container length and height, initial inclination of the surface, and other parameters affecting the nonlinear and inhomogeneous growth process. The increased opportunity for controlling fluids and their instabilities via small forcing or parameter changes in microgravity is notable.
... After sedimentation, positioning of cell aggregates happens in few seconds under the nodes of acoustic standing surface waves. This phenomenon provides excellent systems to study pattern formation due to the high degree of control compared to other pattern-forming systems such as convection or chemical reactions [26], a higher freedom and flexibility over a variety of patterns [27], and the possibility to overcome the above-mentioned limitations of the acoustophoretic devices. In particular, Chen and colleagues have already demonstrated the patterning of spheroids in a number of highly complex geometries and formed microtissues by tuning vibration parameters (frequency and amplitude), fluid properties (viscosity, density, surface tension) and chamber shape. ...
Morphogenesis, a complex process, ubiquitous in developmental biology and many pathologies, is based on self-patterning of cells. Spatial patterns of cells, organoids, or inorganic particles can be forced on demand using acoustic surface standing waves, such as the Faraday waves. This technology allows tuning of parameters (sound frequency, amplitude, chamber shape) under contactless, fast and mild culture conditions, for morphologically relevant tissue generation. We call this method Sound Induced Morphogenesis (SIM). In this work, we use SIM to achieve tight control over patterning of endothelial cells and mesenchymal stem cells densities within a hydrogel, with the endpoint formation of vascular structures. Here, we first parameterize our system to produce enhanced cell density gradients. Second, we allow for vasculogenesis after SIM patterning control and compare our controlled technology against state-of-the-art microfluidic culture systems, the latter characteristic of pure self-organized patterning and uniform initial density. Our sound-induced cell density patterning and subsequent vasculogenesis requires less cells than the microfluidic chamber. We advocate for the use of SIM for rapid, mild, and reproducible morphogenesis induction and further explorations in the regenerative medicine and cell therapy fields.
... These oscillations are due to a parametric resonance between the forcing at the frequency ω and gravity-capillary surface waves with the dispersion relation Ω k ( ), being k a certain wave vector selected as ω Ω = k ( ) /2. Faraday waves have become a paradigmatic example of nonlinear wave systems exhibiting complex periodic 16 and quasi-periodic [17][18][19] dynamics as well as chaotic behaviour [20][21][22][23] . Recently, a number of applications of Faraday waves in the fields outside the area fluid dynamics have been suggested, including novel photonic devices 24,25 , metamaterials 26,27 , alternative sources of energy 28 , and applications in biology 29 . ...
Biological cells and many living organisms are mostly made of liquids and therefore, by analogy with liquid drops, they should exhibit a range of fundamental nonlinear phenomena such as the onset of standing surface waves. Here, we test four common species of earthworm to demonstrate that vertical vibration of living worms lying horizontally on a flat solid surface results in the onset of subharmonic Faraday-like body waves, which is possible because earthworms have a hydrostatic skeleton with a flexible skin and a liquid-filled body cavity. Our findings are supported by theoretical analysis based on a model of parametrically excited vibrations in liquid-filled elastic cylinders using material parameters of the worm’s body reported in the literature. The ability to excite nonlinear subharmonic body waves in a living organism could be used to probe, and potentially to control, important biophysical processes such as the propagation of nerve impulses, thereby opening up avenues for addressing biological questions of fundamental impact.
... The same radially symmetrical resonant wave-patterns have been found on surfaces of water fluids in circular containers, and occur at vibrational modes where whole numbers of waves play a role (Sheldrake Determinants of Faraday Wave-Patterns in Water Samples Oscillated, 2017). The wave phenomena represent a tractable analog model system for the study of morphogenesis (Sheldrake and Sheldrake, 2017). A correlation between Ritz/Chladni frequencies and the proposed algorithmic eigenfrequencies may also be found . ...
... A correlation between Ritz/Chladni frequencies and the proposed algorithmic eigenfrequencies may also be found . Also, the measured eigenfrequencies of water resonances in cir-cular containers (Sheldrake and Sheldrake, 2017) related to high ordered and alternating chaotic patterns in the spectrum of 50 Hz to 200 Hz show similarities with the proposed GM-scale. A first analysis shows a possible fit between both models for about 75% of the measured values. ...
This paper addresses the question whether electromagnetic frequencies associated with pure water are similar to those of biological systems. A literature survey was performed on intrinsic frequencies of water molecules measured across the electromagnetic spectrum using various spectroscopic technologies. The registered frequencies were plotted on an algorithmic generalized music (GM) scale, described by a quantum entangled wave function, and compared with earlier detected electromagnetic frequency patterns revealed in various biological systems. The meta-analysis shows that semi-harmonic frequency patterns found in purified water are very similar to those found in biological systems. A meta-analysis of about 700 measured frequencies of pure water shows that 192 subsequent first and second derivatives of spectral frequency curves of water molecules can be precisely positioned at the proposed lines of the calculated pattern of coherent eigenfrequencies with an error of 0.45% and statistical significance of p < 0.02. A new order parameter characteristic for water molecule assembly has been revealed, which implies quantum coherency and en-tanglement. This is in line with the already evidenced and published universal order that we called the GM-scale. Following these findings, we may assume that water molecule assembly shows electromagnetic and electronic collective states that contain "quantum imprints or molds" for living cells. A potential explanation for this feature is that water molecules are ordered in a partially distorted tetrahedral geometry, which yields a specific network structure. Since water molecules have a comparable distribution of coherent electromagnetic field (EMF) bands to that of fluid assemblies in living cells, a resonant wave interaction is expected between the cytoplasm and surrounding water molecules. Evidence of a new quantum wave equation of coherence for water molecules has been found, that is defined as a physical principle: E n = ħ ω ref 2 n+p 3 m .
