In general, sound waves propagate radially outwards from a point source. These waves will continue in the same direction, decreasing in intensity, unless a boundary condition is met. To arrive at a universal understanding of the relation between frequency and wave propagation within spatial boundaries, we explore the maximum entropy states that are realized as resonant modes. For both circular and polygonal Chladni plates, a model is presented that successfully recreates the nodal line patterns to a first approximation. We discuss the benefits of such a model and the future work necessary to develop the model to its full predictive ability.

In this paper, we utilise optimization methods to determine a frequency-independent phase shift such that two phase-shifted versions of a signal can be summed and the resulting amplitude spectrum is unchanged. A phase difference between two signals is thus defined, which remains constant for all frequencies within a given range. For the intended purpose of this study, we set the frequency range to the audible human hearing range of 16 Hz–20 kHz. We found that a new 3-stage filter method provides a variable phase shifter (i.e., ϕ = 0–360°) without the need for additional amplifiers. In addition, we present a new method that reduces the number of filters necessary, improving both the accuracy and efficiency of current techniques.

Sound reproduction is the electro-mechanical re-creation of sound waves using analogue and digital audio equipment. Although sound reproduction implies that repeated acoustical events are close to identical, numerous fixed and variable conditions affect the acoustic result. To arrive at a better understanding of the magnitude of deviations in sound reproduction, amplitude deviation and phase distortion of a sound signal were measured at various reproduction stages and compared under a set of controlled acoustical conditions, one condition being the presence of a human subject in the acoustic test environment. Deviations in electroacoustic reproduction were smaller than ±0.2 dB amplitude and ±3 degrees phase shift when comparing trials recorded on the same day (Δt < 8 h, mean uncertainty $u$ = 1.58%). Deviations increased significantly with greater than two times the amplitude and three times the phase shift when comparing trials recorded on different days (Δt > 16 h, $u$ = 4.63%). Deviations further increased significantly with greater than 15 times the amplitude and the phase shift when a human subject was present in the acoustic environment ($u$ = 24.64%). For the first time, this study shows that the human body does not merely absorb but can also cause amplification of sound energy. The degree of attenuation or amplification per frequency shows complex variance depending on the type of reproduction and the subject, indicating a nonlinear dynamic interaction. The findings of this study may serve as a reference to update acoustical standards and improve accuracy and reliability of sound reproduction and its application in measurements, diagnostics and therapeutic methods.

Music and sounds elicit a wide range of emotions and activate numerous psychological and physiological effects associated with the functioning of the autonomic nervous system (ANS) and involved in the maintenance of homeostasis. As such, sound interventions can play an important role in supporting human wellbeing and improve outcomes in medical patients. Psychophysiological responses are dependent on the stimulus type, frequency, duration, and spatial conditions of the acoustic environment. To arrive at a more articulate understanding of these dependencies, the effects of singing bowl sounds at 40 Hz, 73 Hz, and 110 Hz were investigated by monitoring physiological, behavioral and emotional responses in healthy adult subjects ( n = 59). Singing bowl sounds were spatially projected in three virtual room sizes (small, medium, large) and eight virtual room shapes (pyramid, tetrahedron, cube, octahedron, dodecahedron, icosahedron, cuboctahedron, and sphere). Overall, exposure to low-frequency singing bowl sounds resulted in a significant increase in positive emotions and a significant decrease in negative emotions across all conditions. Contrary to other studies, we found no discrete effects related to the stimulus type or frequency. Significant differences in electroencephalography (EEG), heart rate variability (HRV) and electromyography (EMG) were consistently dependent on a combination of stimulus frequency and spatial condition, i.e. the resonance of a sound in a room with a particular size and shape. Significant differences in localized EEG power were strongly correlated to localized amplitude deviations of sound waves, while the phase shift of sound wave frequency was predictive of EEG frequency. Significant differences in HR and EMG were strongly correlated to the mean, variability and standard deviation of phase distortions of sound waves. Discrete effects of room shape were observed in galvanic skin response (GSR). Arousal was significantly decreased in a cube and cubeoctahedron, regardless of the frequency. Discrete effects of stimulus duration were observed in GSR and EMG. Arousal was significantly increased during the first 15 min of exposure and significantly decreased until 40 min, regardless of the frequency and spatial condition. We discuss the implications of these findings for future research and therapeutic practices.

In general sound waves propagate radially outwards from a point source. These waves will continue in the same direction, decreasing in intensity, unless a boundary condition is met. To arrive at a universal understanding of the relation between frequency and wave propagation within spatial boundaries, an analysis and comparison is made between the results of Chladni plate experiments and Chladni plate simulations. We consider a finite range of frequencies and plate geometries and present a model that has been shown to successfully recreate the nodal line patterns to a first approximation. We discuss the benefits of such a model and the future work necessary to develop the model to its full predictive capacity.