Study of Resonance and Density in Cymatics
Authors: Kim Huat Yeap1, Abu Bakar Nasir1, Mung Chun Tang1, Tze Guang Tham1, Anthony Brendan1, Sim Yi Tan1
1 Westlake International School, Lot 18662, Jalan Universiti, Taman Bandar Barat, 31900 Kampar, Perak, Malaysia.
Abstract: Cymatics is extensively applied in various fields, particularly in the medication field. This paper delves deeper into the concepts of the Cymatics by analyzing the relation between its resonance and the density of the medium it vibrates in. The conceptual analysis indicates that as density increases, its resonant frequency decreases. With this, an experimental study based on three different mediums has been conducted and the results substantiate the inverse proportionality exhibited in the conceptual analysis. Additionally, the total energy within the Cymatics system is approximated as well, whereby it is noted that the energy level increases in accordance to the increase of density.
Keywords: Cymatics, density, energy, frequency, resonance
Sound has been a major topic of research, be it navigation, communication, medical, music, oceanology, wireless networks, etc. Among the researches, Cymatics has emerged as a recent study of sound with growing interest .
Cymatics is the study of the visualization of sounds in the form of vibrating patterns and its effects. It analyzes sounds from the perspective of wave mechanics. Coined by Hans Jenny in 1967, Cymatics originates from the Greek term ‘kyma’, which means waveform . Jenny discovered that if a plate is vibrated at a specific frequency and amplitude, the shapes and motion patterns of that vibration appear in the material of the plate. When the frequency is increased, the complexity of the patterns increases accordingly. When the amplitude is increased, the motions become more rapid and turbulent. It is learned that the shapes and patterns of sound that appeared pertain to the frequency, amplitude, and intrinsic characteristics of the materials on the plate .
1.1 Applications of Cymatics
Cymatics patterns, which are based on symmetry, play a crucial role in visual perception, design, engineering , as well as numerous relevant applications. Table 1 summarizes some of its latest applications, which include its usages in the fields of medical science, astrophysics, music and arts, as well as oceanology.
As shown in Table 1, one primary application of Cymatics is in the field of medical science. Cymatics therapy has been regarded as an alternative mean of medication. It is exercised to heal illness based on the idea that human tissue is a dynamic energy system operated by a specific vibratory rate. According to Jenny, each cell vibrates at its own natural frequency and subsequently causes a group of cells to vibrate at a set of harmonious frequencies. Any dysfunction of tissue influences the vibration of the set of frequencies and ultimately the natural frequencies of the cells in concern . Cymatics therapy recovers the dysfunction tissue through resonating the disrupted vibration back to its natural frequency. The key of Cymatics therapy lies in the knowledge of how different frequencies influence cells, genes, and other structures of the body.
Triggs reported a list of frequencies that aid in the recovery of certain illnesses . For instance, 0.21 Hz to 2.15 Hz overcomes alcohol addition, 4.11 Hz strengthens the kidney, 38 Hz helps in releasing endorphins in the brain, etc. Cymatics therapy supports the natural healing ability of the body by providing the corresponsive frequencies that are associated with the healthy tissues and organ systems. It uses subtle audible sounds that simultaneously work on an energetic and physical level to provide the body with effective relief for stress, injury, as well as chronic pain .
Apart from this, extensive discussions have taken place with respect to the benefits of integrating Cymatics into interactive systems to allow sensory immersion and control of autistic children. It is revealed in  that autistic children communicate in the form of energy that is inaudible to their parents. Cymatics allows the parents to be able to tune in to the resonance of this energy by assessing the state of silence of their children, which then enables them to visualize their autistic children speak in their particular range of frequencies.
Viewing from the aspect of psychological manifestation,  found that low frequency sound reduces tension and assists relaxation. Natural environment increases the inherent frequencies within the human body, which would in a psychological sense, build up positive emotions, e.g. 147 Hz for love and 205 Hz for happiness .
1.2 Objective of Study
It is noted that researches in Cymatics are mostly based on practical visualizations of the shapes and patterns produced by the sound waves. In conjunction to the importance of Cymatics and the profound applications attributed to it, this paper presents a conceptual analysis of the resonant frequency of the Cymatics system in relation to the densities of varying mediums. Along with its analysis, an experimental study of the resonant frequency in mediums of different densities was also carried out.
- Model Derivation
Cymatics studies sound by connecting sound and matters through vibration into a variety of shapes and forms, dependent on the physical properties of the matter and the frequency of sound . Matter operates in an open system of energy exchange that maintains a steady state far from equilibrium, such that a slight local energetic fluctuation can be amplified to result in massive concatenate effects . Unlike an equilibrium system that requires large amounts of energy to change its state, the energy sensitive nature of matter to self-organize implies that its formations can efficiently adapt to environmental variations inflicted by resonance .
Resonance occurs when energy is supplied in the form of an exciting wave at the natural frequency of the excited system, the Cymatics system in this context. In response, the total energy within the system is efficiently interchanged between the kinetic energy and the potential energy of the vibrating matter, as
where m is the mass of the vibrating matter, v is its speed of vibration, and x is its displacement. k is the spring constant of the oscillating system given as
where ? is the angular velocity.
In general, x is expressed in the form of a cosine wave, as
where xm is the amplitude of displacement, t is the time taken for the wave to travel, and ? is the phase difference. Since v is the rate of change in x, it is derived from differentiating x as
Substituting both x, v, and k into and , yields
where and are the angular frequencies of and , respectively. Therefore,
During resonance, = = . This simplifies as
Since , where is the density of the medium and V is its volume as,
Rearranging the equation and since the resonant frequency of the Cymatics system is, therefore in relation to the density of its medium (?) is found as
(13) indicates that the resonant frequency is proportional to the total energy of the wave propagation in the system and inversely proportional to the density of the medium.
- Experimental Study and Discussion
Based on Cymatics, an experimental study was conducted to verify the relation between the resonant frequency and the density of the medium, as derived in (13). The study is referenced to the work of Ernst Chladni, where he developed a way to visualize the modes of vibration on a flat plate . Chladni reported that resonance is capable of determining a set of unique spatial patterns in response to its fundamental and harmonic modes .
3.1 Experimental Setup
Fig. 1 illustrates the setup of the experiment, where 3 different mediums were tested, namely oil, water and guava juice. The experiment was carried out with a petri dish attached to a 6 W Universal Serial Bus (USB) digital speaker, which is connected to a frequency generator. The speaker supports a frequency range of 90 Hz to 20 kHz. The petri dish has a diameter (d) of 8.5 cm. Each time the experiment is carried out, the corresponding medium is filled into the petri dish with a depth (h) of 0.5 cm. The nodes and wavelengths of the Cymatics patterns appeared on the surface of the medium are observed as the frequency is tuned. Resonance is achieved when the turbulence of the patterns is optimum. In addition, the test on each different medium is repeated for five times and the resonant frequency is noted during each repetition.
3.2 Results and Discussion
The results are shown in Table 2, where the waveforms under the images represent both a time axis and the amplitudes of its vibrations. For the respective medium tested, it is noted that the resonant frequency acquired during each repetition are precise and consistent. The movement of the Cymatics patterns illustrates the phase changes of a material system being ordered by the resonant frequency applied. Sound produced by the frequency generator resonates through the petri dish and introduces an immense energetic fluctuation into the medium. As the emergent patterns defined by resonance are not rigid, but conform to an elastic template that can infinitely alter to consolidate the changing conditions, substantial fluctuations in pattern are observed only on a specific precise frequency, i.e. its resonant frequency.
With this, the waveforms are captured and the amplitude of the waveforms is approximated from the cross-sectional view of the patterns using ImageJ. By applying (13), the total energy of the Cymatics wave is thus calculated. and with respect to ? is as plotted out in Fig. 2. It is learned that as the density of the medium (?) increases, the resonant frequency decreases. This corroborates the relationship derived in (13), whereby the resonant frequency is inversely proportional to the density of the medium. As the density of the medium increases, the corresponding matters propagate at lower velocity (v). Since v = f?, where ? is the wavelength of the Cymatics wave and f is its frequency, as v decreases, its frequency of resonance lowers in accordance.
Conversely, Fig. 2 indicates that the total energy of the Cymatics wave increases as the density of the medium (?) increases. The Cymatics waves demonstrate the concept of matter in association with its energy. Distance between two adjacent nodes varies with respect to the density of mediums and thereby wave lines are formed by the vibrating matters on the node. As resonance drives a denser system, the constant collisions of the tightly organized matter in the system result in the dynamic change of position of nodes and subsequently cause the increased organizational complexity of the Cymatics patterns along with its vibrant variations, which as yet, are too sophisticated to model due to the instantaneous superposition happening on multiple waveforms. This explicates that total energy level of the Cymatics system is directly linked to the density of the medium.
Based on the conceptual analysis of this Cymatics study, it is verified that the resonant frequency is in correlation with the density of the medium. Accordingly, the overall energy of the system is approximated as well. It is to be stressed that the main aim of this study is to analyze the relation between resonance and density by adopting the concept of Cymatics. The three different mediums used in the evaluation are primarily intended to substantiate the validity of the theoretical analysis done. While more samples would affirm the consistency of the study, the samples employed in this work are sufficient in exhibiting the analyzed relationship. In general, it is hoped that the knowledge derived in this study would facilitate the advancement of Cymatics applications in various fields and not simply regarded as a mere display of marvelous patterns.
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