## 1 Introduction  
Helmholtz resonance is known as the phenomenon of air resonating in a cavity, as when one blows over the top of an empty bottle. A container with a small neck and a known volume constitutes the basic building block of a Helmholtz resonator. The compressible fluid in the resonator functions as a spring in the limit when the acoustic frequency is so low that the wavelength is much bigger than any dimension of the resonator [1]. Another parallelism that is used in the literature is that the fluid in the neck serves as an inductor (or mass), while the liquid volume serves as a capacitor (or spring) [2]. Numerous applications of the Helmholtz resonator can be found in the literature. Helmholtz resonators can be used to control noise in aircrafts [3], with the purpose of reducing a duct's transmission loss [4] and mitigating the noise of engines [5] and gas turbines [6]. In addition, Helmholtz resonators can be used for room acoustics, with applications as sound absorbers [7, 8], changing the acoustic behavior of the space which can be evaluated with a suitable source [9, 10, 11] and signal [12]. They have also been used for the same purpose in churches [13] and ancient theaters [14]. Helmholtz resonators can also be used for environmental noise control, increasing the effectiveness of noise barriers [15, 16, 17]. It is also quite common for the Helmholtz resonance to be exploited in the manufacture of bass reflex for speakers [18]. The Helmholtz resonator has extensive application in the study of musical acoustics [19]. The sound of the lowest notes, which are frequently below the frequencies of the lowest strongly excited, acoustically effective, structural resonances, is amplified by a Helmholtz air resonance in almost all hand-held stringed instruments and many bigger ones, such as the concert harp [1]. More recent uses of the Helmholtz resonator can be found in the field of acoustic metamaterials with applications for transmission loss [20], sound absorption [21], as an acoustic superlens [22] or as an ultrasonic metamaterial [23]. In addition, artificial neural networks have been used for the simulation of acoustic properties of resonators [24]. Finally, it can also be used for acoustic energy harvesting [25]. As was previously mentioned, a Helmholtz resonator typically consists of a container with a small neck and a specified volume. However, several modifications in the Helmholtz resonator's design and form have been researched in the literature. For instance, considering the resonator's neck form, variations have been examined such as with a spiral neck [26], with a tapered neck [27], with an extended neck [28] or with an angled neck aperture [29]. Accordingly, variations have been explored regarding the shape of the container [30; 31]. Finally, there are several variations regarding the connection of the parts of the resonator, e.g., neck-cavity-neck-cavity (Dual Helmholtz resonator) [32]. An interesting variation, and also an interesting area of research, is that in which the resonator has more than one neck (usually called multi-neck Helmholtz resonator [33]). The same phenomena is discernible in a situation where there is a leak or a gap in the Helmholtz resonator, which, in this case, can also be called the leakage effect in Helmholtz resonators [34]. [PERSON] et al. [34] have examined the impact of leaks and gaps (i.e., extra necks) in Helmholtz resonators using experimental and computational methods. They noticed that as more necks are added to a Helmholtz resonator's internal baffle, the resonance frequency rises. A similar result is seen when the necks are placed on the resonator's outside surface [35]. Since manufacturing tolerances make it impossible to prevent leaks or gaps in Helmholtz resonators in many real-world applications [34], or perhaps require, for example, drainage of moisture that has accumulated inside the cavity [36], the effect of several necks on Helmholtz resonators must be understood and taken into consideration.