I feel like we are ways out from seeing anything like it. From what I’ve seen non-Newtonian fluids typically take a decent amount of energy to stop something and sound wouldn’t have much energy compared to something like a bullet.
On a sidenote does Decibullz own a patent on percussive hearing protection or am I looking up the wrong term? I feel like there must be other hearing protection out there that is effective against sudden loud sounds.
From some quick searches (so not a definitive answer, but a place to start), it seems that sound waves are most likely longitudinal which doesn’t cause shear. However, shear forces can be created by sound waves when they hit a surface.
From that information, I don’t think the shear energy imparted by a sound wave is very large. Since non-newtonian fluids only thicken under shear, they may not actually behave very differently than a regular fluid in these conditions. Preventing sound waves from traveling is usually accomplished by causing lots of scattering (open cell foam) or by absorbing the energy in a viscoelastic material (usually polymers).