Analysis of Sound
Frequencies: Fundamentals, Applications, and Experiments (Resonance, Particles,
and Patterns)
Análisis de Frecuencias
de Sonido: Fundamentos, Aplicaciones y Experimentos
(Resonancia, Partículas y
Figuras)
Ember Geovanny Zumba Novay*
Manuel Fernando González Puente*
Ana Lucía Tacan Meneses*
Carmen Jhuliana Peña Robles*
ABSTRACT
The
present research offers a rigorous and interdisciplinary analysis of the
concept of frequency, addressing its mathematical definition and its
application in key fields such as acoustics, medicine, electronics, physics,
and astronomy. Frequency, measured in hertz (Hz), constitutes a fundamental
parameter in understanding wave, vibrational, and energetic phenomena. This
basic, qualitative, and experimental study was conducted using a
descriptive-explanatory design, supported by a systematic review academic sources, from which highly relevant articles were selected for
theoretical and practical analysis. Principles of resonance and their
interaction with material structures were explored through a simple experiment involving
a speaker, a membrane made from a balloon fragment, baking soda, and a
cardboard tube (60 cm x 8 cm). This setup enabled the visualization of
resonance patterns (similar to Chladni figures) within the 100 Hz to 936 Hz
range. The results confirm classical theories in acoustics and demonstrate how
specific frequencies can induce the spontaneous organization of particles,
generating structured patterns. MATLAB will be used to perform graphical and
spectral analysis of the observed waveforms, enhancing the scientific
visualization of the data. In addition to its pedagogical and technological
value, the findings support the growing interest in the therapeutic properties
of sound. Various studies indicate that specific frequencies may stimulate
cellular repair processes and emotional balance. As a future research
direction, it is proposed to evaluate how different geometries and materials
influence the formation of complex resonant patterns and their potential
bioenergetic properties.
Keywords:
Frequency, Hertz (Hz), Vibrations, Waves, Physics, Geometric Patterns,
solfeggio
RESUMEN
La
investigación ofrece un análisis riguroso e interdisciplinario del concepto de
frecuencia, abordando su definición matemática y su aplicación en campos clave
como la acústica, la medicina, la electrónica, la física y la astronomía. La
frecuencia, medida en hercios (Hz), constituye un parámetro fundamental en la
comprensión de fenómenos ondulatorios, vibracionales y energéticos. El estudio,
de enfoque básico, cualitativo y experimental, se desarrolló bajo un diseño
descriptivo-explicativo, sustentado en una revisión sistemática en fuentes
académicas, seleccionando artículos altamente relevantes para el análisis
teórico-práctico. Se exploraron principios de resonancia y su interacción con
estructuras materiales mediante un experimento sencillo un altavoz, una
membrana elaborada con un fragmento de globo, bicarbonato de sodio y un tubo de
cartón (60 cm x 8 cm). Esta configuración permitió visualizar figuras de
resonancia (similares a las de Chladni) entre 100 Hz y 936 Hz. Los resultados
confirman teorías clásicas sobre acústica y evidencian cómo ciertas frecuencias
inducen la organización espontánea de partículas, generando patrones
estructurados. Se utilizará MATLAB para realizar el análisis gráfico y
espectral de las ondas observadas, fortaleciendo la visualización científica de
los datos. Además de su valor pedagógico y tecnológico, los hallazgos refuerzan
el creciente interés por las propiedades terapéuticas del sonido. Diversos
estudios señalan que frecuencias específicas pueden estimular procesos de reparación
celular y equilibrio emocional. Se propone, como línea futura de investigación,
evaluar cómo distintas geometrías y materiales influyen en la formación de
patrones resonantes complejos y en su potencial bioenergético.
Palabras clave: Frecuencia, Hercios (Hz), Vibraciones Ondas, Física,
Patrones geométricos, solfeggio
INTRODUCTION
The study of sound frequencies is a fundamental tool
for understanding wave, structural, and energy phenomena on various scales,
from the microscopic level to macroscopic structures. Frequency, expressed in
hertz (Hz), represents the number of cycles per second of a wave, and is a key
quantity in disciplines such as acoustics, electronics, physics, astronomy, and
alternative therapies based on vibration (Jaramillo, 2025). Its analysis allows
exploring how waves interact with matter and contribute to the structural
arrangement of particles, as well as to the energetic modulation in living
organisms.
This research proposes an interdisciplinary approach
to the analysis of acoustic frequencies between 100 Hz and 936 Hz. It
integrates mathematical foundations, resonance physics, computational
simulations in MATLAB and an experimental approach oriented to the
visualization of resonant geometrical patterns. The methodology is based on a
qualitative descriptive-explanatory design, based on a systematic review of 90
academic sources, from which 60 articles with high theoretical and empirical
value were selected.
The central experiment used a low-cost system
consisting of a conventional loudspeaker, an elastic membrane improvised with a
balloon fragment, sodium bicarbonate and a cardboard tube 60 cm by 8 cm in
diameter. By applying specific frequencies using a signal generator, patterns
similar to Chladni figures were observed, where particles were organized
following vibration nodes and antinodes. A range of frequencies was analyzed
including the solfeggio frequencies 432 Hz, 528 Hz, 639 Hz and 936 Hz, recognized
for their harmonizing potential in the field of vibrational medicine (Akimoto
et al., 2018; Benjumea & Castillo, 2022).
MATLAB was used to perform signal plotting, obtain
spectra using Fast Fourier Transform (FFT) and correlate visual results with
spectral data. The analysis confirmed that certain frequencies induce highly
symmetric structured configurations, which could have pedagogical,
technological and biomedical implications.
Beyond the physical validation of the phenomenon, the
results suggest an emerging line of research into the influence of sound
vibration on biological systems. Recent research indicates that frequencies
such as 528 Hz could modulate the autonomic nervous system, induce cell
regeneration processes, and facilitate states of emotional well-being (Ahuja et
al., 2024; Akimoto et al., 2018). These properties justify the growing interest
in integrating acoustic analysis models in disciplines such as energy medicine,
neuroscience and bioengineering.
In the current context, a fragmentation between
theoretical, computational and experimental approaches to the study of
frequencies is observed. While there is abundant literature on the physical
properties of sound, there is still a lack of systematic investigations
exploring how specific frequencies generate ordered geometric patterns in thin
material media. This gap limits the development of applied acoustic
technologies, both in the design of new devices and in their integration with
pedagogical or therapeutic models (Isabel et al., 2024; Arango et al., 2012).
The research proposes an integral analysis model that
allows us to reproducibly observe how sound interacts with matter to produce
visible structural order. The central hypothesis is that the application of
frequencies between 100 Hz and 936 Hz on an elastic membrane covered with fine
particles generates resonant figures that can be interpreted as manifestations
of energy patterns. Through the use of MATLAB and spectral analysis techniques,
we seek to correlate the applied frequency with the resulting geometry,
considering its possible utility in fields such as physics education, acoustic
design of materials and the development of vibrational stimulation
technologies.
Theoretical and Mathematical Foundations
Frequency analysis is based on mathematical concepts
that allow to decompose, represent and study periodic and non-periodic signals
in terms of their harmonic components. In particular, the frequency f, measured
in Hertz (Hz), is defined as the number of complete cycles of a wave occurring
in one second. It is related to the period T by the relation.
(equation 1)
Where T is the time it takes for the wave to complete
one cycle.
1.2 Wave Equation
In physics, the behavior of a harmonic wave in a
medium is described by the wave equation:
(equation 2)
where u(x,t) represents the disturbance, v is the
propagation velocity, x is the position and t is the time. This equation is the
basis for analyzing acoustic phenomena in continuous media.
Fourier series
A periodic function f(t) with period T can be
expressed as the sum of sines and cosines:
(equation 3)
This expansion makes it possible to identify the
fundamental and harmonic frequencies that make up a complex signal, which is
crucial in acoustic analysis and in the generation of specific sounds in
vibrational medicine.
Fourier transform
For non-periodic signals, the Fourier Transform is
used:
(equation 4)
Where F(ω)
represents the spectral density of the signal f(t), and ω=2πf
is the angular frequency. This tool allows transforming signals from the time
domain to the frequency domain, facilitating the spectral study and the design
of acoustic filters or electronic devices.
Wavelength and Physical Relationship
The frequency f, the speed of sound v, and the
wavelength λ are related by:
(equation 5)
In air, v≈343 m/s at room temperature, allowing
specific wavelengths to be calculated for frequencies between 100 Hz and 936
Hz, key in the formation of resonant patterns.
MATLAB application
For computational modeling and signal visualization,
routines in MATLAB are employed, such as:
fft(signal): to obtain the frequency spectrum of a
signal.
spectrogram(signal): to visualize the time-frequency
distribution.
plot(t, y): to plot acoustic waves in the time domain.
sound(y, Fs): to reproduce sounds at different frequencies,
including 432 Hz, 528 Hz and 936 Hz.
These tools will allow you to plot experimentally
generated waveforms, analyze their harmonics and study the behavior of
particles subjected to these frequencies. For this, it is important to know
basic concepts such as frequency, signal, resonance, frequency spectrum and
cymatics.
Frequency
Frequency is a fundamental magnitude in the study of
wave phenomena. It is defined as the number of cycles or repetitions of a wave
per unit time, and is measured in Hertz (Hz). In the context of sound,
frequency determines the perceived pitch: low frequencies are associated with
low-pitched sounds, while high frequencies generate high-pitched sounds. From a
mathematical perspective, frequency is related to the periodic function
describing the wave, and its analysis allows identifying harmonic components and
interference phenomena. In this research, the range between 100 Hz and 936 Hz
is considered, covering both fundamental frequencies and those that have been
linked to harmonic and therapeutic properties.
Signal
A signal is the representation of a physical quantity
that varies in time and contains information. In acoustic frequency analysis, a
sound signal is a function of time describing the variation in air pressure
caused by a vibratory source. Signals can be analyzed in the time domain or in
the frequency domain. In this study, pure sinusoidal signals are generated by a
frequency generator and applied to a vibrating membrane. These signals are also
modeled and plotted in MATLAB, which allows studying their spectral
characteristics and their ability to induce resonant patterns in particulate
materials.
Resonance
Resonance is a physical phenomenon that occurs when a
system is excited by a specific frequency that coincides with its natural
frequency of vibration. Under this condition, the oscillation amplitude of the
system increases significantly, allowing highly efficient energy transfer. In
acoustic systems, resonance can be observed in musical instruments, sound
cavities and mechanical structures. In this study, resonance is induced in an
elastic membrane using specific frequencies. The result of such resonance is
the appearance of defined geometric patterns, reflecting nodes and antinodes of
vibration. This behavior is key to understanding how certain frequencies
generate order in matter.
Frequency spectrum
The frequency spectrum is the representation of the
frequency components that make up a signal. It is usually obtained through the
Fourier Transform, which decomposes a signal into its different harmonic
frequencies. Spectral analysis makes it possible to visualize which frequencies
are present in a signal and with what amplitude. In this research, MATLAB is
used to generate and analyze spectra of the applied signals, in order to
correlate the theoretical data with the physical patterns observed in the experiment.
This tool is essential to validate the correspondence between the frequency
content of the signal and the structure of the induced resonant patterns.
Cymatics
Cymatics is the study of the visible effects of sound
on matter. This interdisciplinary field explores how acoustic waves can
organize fine particles, liquids, or flexible surfaces into ordered
patterns.These patterns, known as Chladni figures or cymatic figures, are
formed by the action of stationary nodes that emerge during resonance. Cymatics
provides a visual window into the behavior of sound waves, allowing us to
observe how vibrational energy structures matter. In this work, cymatics is
applied as an experimental tool to visualize the impact of specific frequencies
on the formation of resonant geometries, which has not only physical, but also
pedagogical and potentially therapeutic implications.
MATERIALS
AND METHODS
The research adopts a qualitative approach with a
descriptive and experimental design, aimed at understanding the formation of
resonant patterns generated by specific acoustic frequencies. The study was
structured in two complementary phases: a theoretical-computational phase and
an experimental phase.
In the theoretical-computational phase, a review of
the mathematical, physical and acoustic fundamentals that explain the resonance
phenomenon was carried out. Based on these concepts, simulations were developed
using MATLAB software, using functions such as fft, spectrogram and plot to
represent frequency spectra, visualize harmonic components and model the
propagation of sound waves. The purpose of this stage was to anticipate the
expected geometrical patterns and to establish a comparative basis with the
experimental results.
The experimental phase consisted in the construction
of a simple, inexpensive and replicable setup. The system included a
loudspeaker connected to a mobile frequency-generating application, an elastic
membrane improvised with a balloon fragment, a cardboard tube 60 cm long and 8
cm in diameter, and sodium bicarbonate as particulate material. Frequencies
between 100 Hz and 936 Hz were applied, including solfeggio frequencies such as
432 Hz, 528 Hz, 639 Hz and 936 Hz, recognized in the literature for their supposed
ability to generate harmonic order.
For each frequency applied, the formation of geometric
figures was documented by means of photographs, repeating each test three times
under controlled environmental conditions to ensure the validity of the data.
Subsequently, the patterns obtained were compared with the models generated in
MATLAB to evaluate the degree of correspondence. This integrative methodology
allows linking theory, simulation and direct observation, facilitating a deeper
understanding of how acoustic frequencies induce ordered structures in matter
through the phenomenon of resonance.
RESULTS
The experimentation carried out showed a clear
relationship between the applied sound frequency and the formation of geometric
patterns on an elastic membrane covered with sodium bicarbonate. Frequencies
between 100 Hz and 936 Hz were applied, and it was observed how each frequency
generated a different vibrational configuration, which could be directly
visualized by the organization of the particles. This phenomenon can be
explained by resonance, in which particles tend to distribute themselves in
vibrational nodes and antinodes when the applied frequency coincides with the
natural frequency of the system (Arango, Escobar & Reyes, 2012; Jaramillo,
2025).
At low frequencies such as 100 Hz, the patterns were
simple, predominantly circular, and with particle accumulation at the membrane
edges, indicating low nodal complexity. This is consistent with previous
studies in acoustic physics, where it is noted that low frequencies tend to
generate vibrational modes of lower energy and spatial division (Peláez, 2021).
As the frequency increased, especially in the cases of
216 Hz, 432 Hz and 528 Hz, more complex and symmetrical geometric patterns were
generated. The particles were organized in clear divisions, with visible nodal
lines separating vibrating zones from stationary zones, replicating the
well-known Chladni figures (de la Plaza Villarroya, 2023; Villarroya, 2023).
This behavior was not only visually consistent, but was also reflected in the
spectra obtained by Fast Fourier Transform (FFT), which showed sharp and narrow
peaks at the target frequencies, validating the purity and stability of the
signals (MATLAB, 2025; Alarcón, 2000).
The 432 Hz and 528 Hz frequencies stood out in the
analysis for their ability to generate stable, repetitive and highly organized
harmonic structures. These frequencies, in addition to their physical behavior,
have been associated with bioenergetic and harmonizing effects in various music
therapy and applied neuroscience studies (Akimoto et al., 2018; Benjumea &
Castillo, 2022). In the present experiment, their structuring impact was
confirmed by the observation of symmetrical and easily reproducible patterns,
suggesting that these frequencies possess a special resonant potential.
The validity of these results is reinforced by the
correspondence between the observed physical patterns and the computational
simulations performed in MATLAB. The plots of the 432 Hz and 528 Hz sinusoidal
signals, together with their respective spectra, showed clear harmonic
components, with no significant distortions or secondary harmonics (MATLAB,
2025). This coincidence suggests that the conditions of the experiment-pure
frequency, constant membrane voltage, and controlled environment-were adequate to
induce stable resonance.
Another important finding was the specific response of
the particles to sound. As higher frequencies were applied within the set
range, the resulting patterns showed a higher density of nodes and a more
complex distribution of antinodes. This behavior aligns with theoretical
principles of acoustics and spectral analysis, where it is established that, at
higher frequencies, the vibrational modes of physical systems tend to split
into smaller and more symmetric regions (Meléndez, 2021; Barba Maggi, 2025).
Taken together, these results not only validate
resonance theory from a visual and experimental approach, but also confirm that
the application of acoustic frequencies can induce order in material systems.
This finding has implications both in the educational field and in biomedical
and technological research. From a pedagogical point of view, it allows the
visualization of abstract concepts of physics through a tangible experience.
From a scientific perspective, it opens the way towards the development of acoustic
technologies for the structural modulation of materials or therapeutic
applications using sound vibrations (Martínez-Lozano et al., 2023; Siesto
Sánchez, 2017).
The use of solfeggio frequencies, especially 432 Hz
and 528 Hz, supports lines of study investigating their impact beyond the
physical structure, exploring the relationship between sound, form and
well-being. While this study focused on frequency-induced geometric
manifestation, its convergence with therapeutic literature suggests fertile
ground for future research combining physical, perceptual, and biological
analysis.
|
Figura
1.1. Globo Fuente: Autores |
Figura
1.2. Bicarbonato Fuente:
Autores |
Figura
1.3. Parlante con el tubo y el bicarbonato Fuente: Autores |
|
|
Figura
1.4 Frecuencia 100Hz Fuente: Autores |
Figura
1.5. Frecuencia 216 Hz Fuente: Autores |
||
|
Figura
1.6. Freucnecia 432 Hz Fuente: Autores |
Figura 1.7. Frecuencia 528 Hz Fuente: Autores |
||
|
Figura
1.8. Frecuencia de 430 Hz Fuente: |
Figura 1.9. Frecuencia de 320 Hz Fuente: |
||
Higher frequencies, such as 639 Hz, 741 Hz and 936 Hz,
generated more complex patterns, with fine geometric structures and high
symmetry. In some cases, the particles formed mandala-like figures, which
reinforces the hypothesis that specific frequencies induce order and
organization in matter.
|
Figura
1.10. Frecuencia 639 Hz Fuente: Autores |
Figura
1.11. Frecuencia 741 Hz Fuente: Autores |
Figura
1.12. Frecuencia 936 Hz Fuente: Autores |
Figure 1.13. Gráfica de frecuencias construida en MatLab
Fuente:
Autores
The implementation of MATLAB software in this research
allowed a detailed spectral analysis of the applied acoustic signals, which was
essential to validate the purity and stability of the frequencies used in the
experiment. Each signal was modeled as a simple sinusoidal function, and
subsequently analyzed using the Fast Fourier Transform (FFT), a mathematical
tool that decomposes a complex signal into its frequency components (Enrique
Alarcón, 2000).
The generated spectra revealed narrow, well-defined
peaks centered on the target frequencies, which confirmed the stability and
cleanliness of the signals generated by the mobile application used as
frequency generator (MATLAB, 2025). This precision allowed establishing a
direct relationship between the applied frequency and the geometric pattern
observed in the elastic membrane covered with sodium bicarbonate, since the
peaks in the frequency domain coincided with the appearance of ordered
structures in the physical domain.
It was further evidenced that the clarity and symmetry
of the resonant patterns were directly related to the signal stability and
uniform membrane tension. Under constant conditions, the figures obtained were
reproducible with minimal deviation, which gives reliability to the
experimental design and the method of analysis (Barba Maggi, 2025; Arango et
al., 2012).
Particular attention deserves the 432 Hz and 528 Hz
frequencies, which not only generated remarkably organized patterns, but have
also been widely studied for their harmonizing effects in vibrational medicine
and music therapy contexts (Akimoto et al., 2018; Benjumea & Castillo,
2022). These frequencies showed pure and stable spectral peaks, and their
associated physical patterns presented well-defined nodes and symmetries,
reinforcing the hypothesis that certain tones possess more pronounced structuring
properties.
The combination of computational modeling and spectral
analysis using MATLAB with the empirical observation of physical patterns
allows not only to validate the experimental results, but also to open new
lines of exploration on the harmonic behavior of sound frequencies in
educational, therapeutic and technological contexts (Siesto Sánchez, 2017; de
la Plaza Villarroya, 2023).
DISCUSSION
The present study, combining theoretical,
computational and experimental approaches, confirms the hypothesis that
specific acoustic frequencies can induce order in material systems through
resonance. Geometric pattern formation, visually observed and computationally
validated with MATLAB, supports both classical theories in acoustic physics and
new perspectives in vibrational medicine, structural design and scientific
pedagogy (Arango, Escobar & Reyes, 2012; Meléndez, 2021).
One of the key findings was the clear correlation
between the applied frequency and the geometric complexity of the patterns
generated on the elastic membrane covered with sodium bicarbonate. Low
frequencies, such as 100 Hz, resulted in simple and poorly defined patterns.
However, with increasing frequency, especially at values such as 432 Hz and 528
Hz, highly organized figures were observed, with symmetrical and repetitive
structures, confirming that certain tones induce a higher degree of order and resonance
(Jaramillo, 2025; MATLAB, 2025).
The application of the Fast Fourier Transform (FFT)
allowed evidencing that the generated signals were pure, with well-defined
narrow spectral peaks. This spectral precision is crucial to ensure that the
observed patterns are due only to the applied frequency and not to unwanted
noise or harmonics (Alarcón, 2000; Benjumea & Castillo, 2022). In this
sense, the coincidence between the empirical results and the computational
simulations reinforces the reliability of the experiment.
The observed phenomenon has a theoretical explanation
based on classical physics: when an acoustic wave coincides with the natural
frequency of vibration of a system, resonance is produced, which generates
stationary nodes and antinodes in which particles accumulate or disperse. These
nodes, when visualized with materials such as bicarbonate, form Chladni
figures, the study of which has been widely used to understand how vibrations
structure matter (de la Plaza Villarroya, 2023; Villarroya, 2023).
In particular, frequencies such as 432 Hz and 528 Hz,
in addition to their resonant behavior, have been widely discussed in
alternative and scientific literature for their association with biological and
psychological benefits. Akimoto et al. (2018) evidence that 528 Hz frequency
can modulate the autonomic nervous system and enhance endocrine processes. This
coincides with the results obtained in the present study, where this frequency
generated harmonic patterns of high complexity and stability, even after
multiple repetitions.
Table 1.1. Most recognized healing frequencies
|
Frecuencia (Hz) |
Nombre/Asociación |
Efecto terapéutico |
Sonido |
|
174 Hz |
Base/Alivio físico |
Reduce el dolor, estabiliza órganos |
|
|
285 Hz |
Regeneración celular |
Reestructura tejidos, piel
y órganos |
|
|
396 Hz |
Liberación del miedo |
Elimina bloqueos y traumas |
|
|
417 Hz |
Cambio y transformación |
Limpia energía negativa |
|
|
432 Hz |
Frecuencia universal |
Armoniza el cuerpo y la naturaleza |
|
|
528 Hz |
ADN y amor |
Reparación genética, paz
interior |
|
|
639 Hz |
Relaciones armónicas |
Mejora comunicación, empatía |
|
|
741 Hz |
Desintoxicación |
Limpia células y órganos |
|
|
852 Hz |
Intuición espiritual |
Conexión con el yo superior |
|
|
963 Hz |
Frecuencia divina |
Activación de la glándula
pineal |
|
Fuente: Autores
Note: The table is constructed with the
links to the different healing frequencies that are extracted from YouTube.
Table 1.2.
Description of resonant patterns generated by specific frequencies on an
acoustic membrane.
|
Frecuencia (Hz) |
Descripción del Patrón y
Comportamiento |
Interpretación /
Aplicación Potencial |
|
174 Hz |
Patrones de baja
complejidad. Movimientos suaves del bicarbonato. |
Baja energía vibracional.
Relajación muscular y alivio del dolor. |
|
285 Hz |
Estructuras más definidas. |
Resonancia en tejidos blandos. Posible regeneración y
reparación celular. |
|
396 Hz |
Figuras circulares
concéntricas. |
Simetría radial. Asociada
a liberación emocional. |
|
417 Hz |
Patrones espiralados con mayor movilidad del
bicarbonato. |
Reorganización estructural. Estimula el cambio y la
renovación. |
|
432 Hz |
Figuras simétricas, suaves
y armónicas. |
Frecuencia natural.
Equilibrio físico y energético. |
|
528 Hz |
Patrones geométricos complejos, nodos de acumulación. |
Reparación del ADN. Alta eficiencia vibracional. |
|
639 Hz |
Estructuras florales y de
simetría elaborada. |
Armonización de
relaciones, apertura a la comunicación. |
|
741 Hz |
Dispersión caótica del bicarbonato si no se modula. |
Limpieza energética. Puede usarse para
desintoxicación física y emocional. |
Fuente:
Autores
Table 1.3.
Relationship between frequency, wavelength and expected nodal complexity.
|
Frecuencia (Hz) |
Longitud de Onda (λ) (m) |
Tipo de Patrón Nodular Esperado |
Complejidad del Patrón
Cimático |
|
174 Hz |
1.97 |
Ondas amplias y simples,
nodos lejanos |
Baja |
|
285 Hz |
1.20 |
Ondas más densas, inicio de geometría radial |
Moderada |
|
396 Hz |
0.87 |
Círculos concéntricos o
estructuras radiales |
Moderada–Alta |
|
417 Hz |
0.82 |
Espirales o estructuras rotacionales |
Alta |
|
432 Hz |
0.79 |
Mándalas, patrones
hexagonales o florales armónicos |
Alta |
|
528 Hz |
0.65 |
Geometría fractal, estructuras simétricas complejas |
Muy Alta |
|
639 Hz |
0.54 |
Figuras florales
múltiples, nodos vibrantes |
Muy Alta |
|
741 Hz |
0.46 |
Geometría difusa o caótica, nodos irregulares |
Alta / Caótica |
Fuente: Autores
Note: v = 343m/s is the speed of sound in air.
In addition, the resulting figures associated with
frequencies such as 639 Hz and 936 Hz were characterized by their floral
symmetry and mandala-like appearance, which has also been described in
literature on vibrational medicine as symbols of energetic harmonization and
emotional restructuring (Siesto Sánchez, 2017). This type of visible resonance
suggests that, beyond physical behavior, frequencies could induce positive
psychoemotional effects, which has been explored by authors such as Benjumea
& Castillo (2022) in the field of music therapy.
At the methodological level, the simplicity of the
experimental setup, composed of inexpensive and accessible elements,
demonstrates that expensive equipment is not required to observe complex
acoustic phenomena. This positions the present study as a high-impact
pedagogical tool, ideal for teaching concepts such as frequency, wave,
resonance and spectrum. As stated by Arango et al. (2012), direct visualization
of sound strengthens the intuitive understanding of phenomena that are usually
approached abstractly.
On the other hand, the use of the cardboard tube as a
resonator is a remarkable innovation. This component acted as an acoustic
cavity that concentrated sound energy, amplifying certain frequencies depending
on its geometry. This principle, used in wind musical instruments, was
creatively applied here to reinforce the visualization of resonant nodes (Cros
& Ferrer-Roca, 2011).
The present work also provides evidence for future
technological developments. The identification of frequencies that generate
complex and reproducible geometric structures can be used in the design of
acoustic devices, sound control interfaces, vibrational sensors and
non-invasive diagnostic mechanisms, as suggested by Martínez-Lozano et al.
(2023). Likewise, in the field of biomedical engineering, these frequencies
could be applied in non-pharmacological therapies that stimulate cellular
processes by means of vibration, as suggested by Ahuja et al. (2024).
A noteworthy aspect is the possibility of using these
frequencies in therapeutic and meditation settings. Empirical evidence shows
that certain frequencies not only generate physical order, but could also
induce states of calm, introspection or well-being. This coincides with
findings reported by Sanchez (2017), who studies the influence of musical art
on human biology, and by Akimoto et al. (2018), who relate sound to
neuroendocrine processes.
It is important to note, however, that while the
results obtained are promising, the research focused exclusively on the
observation of physical patterns. No tests were performed on living tissues, so
the possible therapeutic effects mentioned should be interpreted with caution.
Future studies could combine mechanical resonance and bioimaging techniques to
evaluate how these patterns affect cells, tissues, or organisms, as suggested
by the line of work of Martínez-Lozano et al. (2023).
Finally, the visual richness and repeatability of the
experiment opens a range of possibilities to extend this model to new membrane
geometries, other particulate materials and different types of signals. For
example, the combination of binaural sounds, amplitude modulation or complex
musical signals would allow us to observe whether they also induce geometric
order, which would constitute an advance towards a new science of sound-induced
shape (Villarroya, 2023; UNESCO, 2025).
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*Ingeniero de
Mantenimiento - Ingeniero en Administración y Producción Industrial- Magister
en Diseño Industrila y de Procesos - Magister en Educación Tecnologia e
Innovación – Docente de la Escuela Superior Politécnica de Chimborazo - ESPOCH,
Riobamba, Ecuador
ezumba@espoch.edu.ec, https://orcid.org/0000-0002-2121-8418
* Ingeniero de
Mantenimiento - Magister en Gestión de la Educación Mención en Educación
Superior. Escuela Superior Politécnica de Chimborazo - ESPOCH
https://orcid.org/0009-0002-5498-2698
* Doctora en
Contabilidad Superior y Auditoria.
Magister en Educación Innovación y Tecnología
https://orcid.org/0000-0003-3942-9798
* Ingeniera en Contabilidad y Auditoría -
Magíster en Educación- Mención Pedagogía