## 1 Introduction  
Over the past several decades, dynamic-mode cantilever sensors have been studied extensively with broad applications in various fields due to their fast response and low fabrication cost. In addition, with the development of microfabrication technology, high sensitivity and resolution are realized [1]. This kind of sensor mostly detects the resonant frequency shift induced only by the added mass effect, so sensitivity improvements are usually realized by decreasing the size or operating at higher order modes [2; 3], which may bring manufacturing complexities and frequency measurement difficulties. To conquer these deficiencies, sensing architecture based on Helmholtz resonance was proposed in our previous paper as a new type of biosensor [4], which shows a higher sensitivity at a similar operating frequency compared with the sensor using a cantilever beam. However, when the amount of test sample is limited (which is common in biosensor application), the operating frequency tends to be much higher, which brings challenges in resonance excitation and frequency measurement. In this paper, we aim to design a new type of Helmholtz resonator (HR) to lower the resonant frequency. Since the HR is known as an effective muffler, in the field of noise control in practical architecture or vehicle engineering, some research was carried out to lower the resonant frequency of HRs for better noise attenuation performance at low frequencies under a space restriction. [PERSON] and [PERSON] [5] investigated the acoustic performance of HRs with an extended neck and found that the extension of the neck into the cavity can lower the resonant frequency without increasing the volume. [PERSON] et al. [6] then studied HRs with fibrous material and found that the acoustic performance can be modified considerably using the fibrous material without changing the cavity dimensions. [PERSON] et al. [7] constructed the low-frequency noise attenuation technology using HRs with horn-shaped necks. [PERSON] and [PERSON] [8] modified HRs using a spiral duct to lengthen the neck in a small space, showing that HRs with a spiral neck can achieve high noise attenuation performance at low frequencies. [PERSON] et al. [9] compared the noise attenuation effect of an HR with an extended neck and an HR with a spiral neck and explained the potential application of these two neck types in noise control. [PERSON] et al. [10] studied HRs with a flexible end plate and found that the flexible plate provided the modified HRs with multiple resonant frequencies, while the fundamental frequency went to a much lower frequency. [PERSON] et al. [11] applied the multi-objective optimization procedure to HRs with a flexible end plate, which can produce a small volume HR capable of achieving high transmission loss across a specified frequency range. [PERSON] and [PERSON] [12] proposed a meta-surface composed of a perforated plate with a hole and a coiled air chamber, by which sound absorption could be achieved in a low frequency range. [PERSON] and [PERSON] [13] proposed an HR with a flexible membrane on an elastic foundation for the measurement of the elastic coefficient of human skin. The elastic coefficient of human skin is related directly with the resonant frequency located between rigid HRs and HRs with a flexible membrane, by which the corresponding elastic coefficient value can be obtained. In this paper, a modified Helmholtz resonator with an Archimedes spiral neck filled with two kinds of fluid was proposed for the measurement of the analyte concentration in aqueous solution at low frequency. The equivalent mass-spring system was used to predict the resonant frequency of an HR with a spiral neck, by treating the Archimedes spiral neck as a straight neck with the equivalent length. An analytical example was analyzed and verified by acoustic finite element analysis, and based on that, the measurement principle was proposed and the sensing system was established.