Diffuseness quantification in an acoustic test chamber using the isotropy derived by the angular spectrum of sound waves based on the spherical harmonics expansion

Spacecraft are exposed to acoustic loads during flights to space by launch vehicles. The endurance of spacecraft structure is verified by a ground acoustic test specified in test standard documents of the aerospace community. These standard documents require the execution of ground acoustic tests in a reverberant chamber on the assumption that it can generate a diffuse sound field which is normally defined as “completely isotropic and equal probability of energy flow in all directions”. However, in the space development industry and related studies, the directions of incident sounds which cause non-diffuseness has not been identified by the experimental comparison with the theoretical values of an ideal diffuse sound field (e.g. reverberation times, homogeneity of sound pressures and spatial correlation functions). Therefore, the conventional standard documents do not clearly specify the quantitative requirements regarding the directional properties of sound fields inside reverberant chambers. To specify the quantitative requirement on the directional properties of sounds, this paper focused on calculating the degree of isotropy of a sound field by the direct measurement of directional properties of sound waves as angular spectra. In this paper, the method to obtain the angular spectrum based on the theory of the expansion of the plane wave into spherical harmonics by using a spherical microphone array was firstly combined with the existing formula of the isotropy indicator, which allowed us to determine the frequency range when we apply the combined method to sound fields. The method to determine the applicable frequency range was demonstrated and the process of obtaining the angular spectrum and isotropy indicator was verified by numerical simulation. Finally, the combined method was applied to the sound field in the reverberant chamber of JAXA 1600m3 acoustic test facility.