# Review of Acoustic Sources Alternatives to a Dodecahedron Speaker
## 1 Introduction
### Dodecahedron Speakers  
The most common practical implementation of a pulsating sphere producing an omnidirectional field is a dodecahedron speaker. As [PERSON] states [27]: \"its radiation characteristics (pulsating sphere) can be approximated within certain limits by a regular dodecahedron or icosahedron composed of 12 or 20 regular polygons, respectively, each of them fitted out with a loudspeaker in its center\". However, commercial implementations exist mainly for the dodecahedron speakers and less for the icosahedron speakers. Dodecahedron speakers are omnidirectional sources widely used for room acoustics measurements. Commercially available dodecahedron speakers are manufactured and tested in order to meet the ISO 3382-1 sound source requirements. The omnidirectional directivity is approached by placing 12 electrodynamic loudspeakers (direct radiator type) in a regular 12-face polyhedron. The dodecahedron speaker, in essence, is a \"dodecahedron arrangement of drivers to approximate the omnidirectional sound radiation characteristics of a monopole\" [28]. However, other polyhedron loudspeakers can also be used which in some cases can be viewed as equally omnidirectional [29]. In practice, since dodecahedron speakers cannot emit sufficient acoustic power if an impulsive signal is applied directly, alternative excitation signals are used. The most common ones are maximum-length sequence (MLS) [22] and exponential sine sweep (ESS) [30] which are described in Annex A and B of ISO 18233 [31], respectively. Application of these methods ensures that the loudspeaker can emit a large amount of energy with longer duration without challenging its limited peak power capability, while impulse responses with a high time resolution can still be obtained afterward through post-processing. These deterministic excitation signals can be accurately reproduced and thereby enhance the repeatability of the measurements. Since the dodecahedron speaker utilizes MLS or ESS signals, enhancement of the signal-to-noise ratio by 20 dB to 30 dB or more compared to the classical method may be obtainable, as ISO 18233 [31] states. However, as ISO 18233 also states, the use of loudspeakers typically introduces non-linear distortion in the system which increases with the excitation level and violates the requirement for linearity, hence appropriate signal levels should be chosen. Optimum signal-to-noise ratios can be found in [PERSON] et al. [32], while comparison of the two methods can be found in [33]. The appropriate choice of excitation signal for acoustic measurements can be depended on the background noise [34]. Drawbacks of Dodecahedron Speakers  
Despite the widespread use of dodecahedron speakers, there are certain drawbacks associated with them. Namely, we can say deviation from omnidirectionality, low-frequency performance and practical reasons such as high cost. The dodecahedron speaker fails to be an exact approximation of a monopole source since there is a deviation from omnidirectionality. The directivity of a dodecahedral loudspeaker can be considered uniform in the low-frequency range, while at higher frequencies (namely above 1 kHz), sound radiation shows greater deviation [26]. Because of the finite difference in distance between the loudspeaker diaphragms as well as the fact that these usually have a conical shape and are not a continuous part of the spherical surface, the radiation pattern is not ideally spherical at frequencies where the distance between loudspeakers or the depth of the cones are larger than a small fraction of the wavelength. Typically, the deviations start to become large when \(ka>3\), where \(a\) is the radius of the sphere and \(k\) is the wavenumber [35]. These deviations seem to increase, the smaller the measuring distance from the sound source inside the critical distance [36].