This paper reports on an acoustic planar notch filter with a sub-wavelength thickness at the notch frequency. The developed notch filter consists of a number of spherical Helmholtz resonators (HRs) connected to a hole created in a plate. The HRs were placed at the in-plane vertices of a regular polygon. A simulated pressure distribution revealed that this uniform arrangement of HRs improves the silencing effect because the uniform applied waves emitted from the HRs act as canceling waves to the cross-section of the short hole (in this case, the length of the hole is sub-wavelength). The total pressure emitted from the HRs is equal regardless of the number of HRs connected to the hole. Therefore, the arrangement of HRs is essential for realizing a planar notch filter. Simulated transmittance spectra showed that the depth of the dip in the transmittance increased with the number of uniformly arranged HRs. We confirmed that the experimental transmittance spectra of fabricated notch filters, which consisted of between one and six HRs, agreed with the simulated transmittance spectra. The design of the acoustic filter presented in this study and the corresponding analysis should motivate further development of thin acoustic filters.
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