Abstract
We have investigated the distribution of sound pressure levels in the Helmholtz resonators over a wide range of frequencies. Computer simulation of the sound field at the resonator was performed by using a finite element method and an experimental research.We have established the existence of many resonance frequencies at the resonator and show the distribution of the maxima and minima of sound pressure levels within the volume of the resonator. It has been revealed that the distribution of the resonator's resonance frequencies does not obey the harmonic law. That makes it possible to consider resonance properties of the resonator similarly to the oscillations in a membrane or a bell. The second resonance frequency of the resonator is 6‒9 times higher than the first resonance frequency corresponding to the Helmholtz resonance. Simulation of sound field in the resonator showed the presence of nodal lines in the distribution of the sound pressure in both the resonator's volume and its throat. It has been established that the number of nodal lines for the first frequencies is one unity less than the resonance number.A common feature to all distributions is that when a measuring point approaches the edge of the resonator throat, the level of sound pressure decreases. In addition, the study has found the possibility to generate resonance only within the resonator's volume without distinct nodal lines in the throat.Comparative analysis of data acquired from experiment and during computer simulation has revealed a high level of reliability of the results obtained. Error in determining the resonance frequency did not exceed 0.8 %. That makes it possible, when further determining the sound field in the systems of resonators, to employ computer simulation instead of resource-intensive experimental studies.The existence of many resonances at the Helmholtz resonator enables the construction of broadband devices, which could be based on using a given type of resonators
Highlights
Research into analysis of human sound sensations began in the mid-19th century [1]
The presence of active resistance is predetermined by the friction between air and the walls of the throat and by losses in the oscillatory energy due to the radiation of sound by an open end of the throat [2]
The Helmholtz resonators were used to analyze the spectra of complex sounds before the advent of computing technology, they were applied in temple structures for the correction of acoustic properties of premises
Summary
Research into analysis of human sound sensations began in the mid-19th century [1]. Even though a given work belongs to the field of psychoacoustics, a need arose during its execution to use and register the phenomenon of resonance. In terms of electric acoustics, they represent an acoustic oscillating system, consisting of flexibility, mass, and active resistance. In this case, the flexibility is the air inside the container, the mass is the air that fills the narrow resonator throat, and the attached mass of air adjacent to the end of the throat. The Helmholtz resonators were used to analyze the spectra of complex sounds before the advent of computing technology, they were applied in temple structures for the correction of acoustic properties of premises. One of the areas where resonators could be employed is the construction of focusing systems for acoustic medical instruments or flaw detection devices with simultaneous amplifying properties. The existence of multiple resonance frequencies in the resonator makes it possible to use them in broadband acoustic systems
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