Wave propagation in multiply scattering media is a fundamental and long-standing topic that has undergone renewed interest with the advent of metamaterials. In particular, disorder control is an efficient way to alter wave propagation. Stealth hyperuniform (SHU) media, characterized by the cancellation of large-scale density fluctuations, have proven particularly relevant in this context. The objective of this article is to show that the remarkable properties of these media are robust to many material constraints and are therefore a very relevant avenue for the control of mechanical waves, i.e., acoustic waves in fluid media and elastic waves in isotropic solids. Furthermore, this article provides theoretical insights by reformulating multiple scattering correlation integrals through the radial structure factor $S\left(q\right)$. This spectral approach explicitly demonstrates that transparency in SHU media arises from the exact cancellation of the monopole scattering mode by positional correlations. We formally demonstrate the existence of a transparency regime for elastic waves in solids. We show that this phenomenon is remarkably robust against mode conversions and, crucially, is governed by two distinct cutoff frequencies for longitudinal and transverse waves. Our results establish a comprehensive framework for wave control in correlated disorder, from transparency to mechanical waves to the emergence of Bragg-induced attenuation peaks.

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• Acoustic modeling
• Wave scattering
• Acoustic metamaterials