Materials that behave as "metals" for sound waves? Probably the most well known property of metals are that they are shiny. Ultimately arising from the high density of conduction electrons capable of carrying current, this shinyness is means that metals are broadband reflectors of light from radio frequencies to visible light (until about the plasma frequency). The question is, why aren't there many materials that act as metals for sound (i.e. near perfect broadband reflectors) just as there are for electromagnetic radiation? Clearly such materials would be pretty useful for audio engineering purposes, so there's a clear commercial motivation for finding them, but I don't know of any examples
This question came up as I was teaching an intro physics course and actually stumped me, I couldn't come up with a simple and powerful explanation that such a question deserves. My first instinct was to think of the long wavelengths of sound compared to light, but that doesn't seem like it's enough.
Edit: There's this relevant paper I found on the topic https://arxiv.org/abs/2010.02813
The explanation there is the impedance mismatch between air and solids, but that doesn't make much sense to me since there's a similar mismatch in the case of electromagnetic waves.
 A: The two are not as closely related as it appears.
The defining property of a metal is electrons in the conduction band.
In some materials, an electron can be promoted to an excited state where it does not stick to individual atoms. Instead, it spreads out across multiple atoms. It can easily move. The energy levels in atoms are discrete and well separated. By contrast the spread out energy levels are very closely spaced. There are many states with very nearly the same energy. Instead of an many individual atoms with orbitals that the same energy level, these materials have bands of states.
If an electron is promoted into a band, it can move easily. But bands are often empty because they are at energies higher than the highest ground state electron.
In some materials like Si or GE, the band is a small distance above the highest ground state. A few electrons are promoted because of thermal energy. These have a few electrons that can move easily. They are semi-conductors.
In metals, empty conduction band states start right at the highest ground state energy. Electrons can easily be promoted by thermal energy. There are many electrons in the conduction band that can easily move. These are conductors. Since electrons carry kinetic energy as well as charge, they conduct heat as well as electricity.
When light hits a metal, the electrons are vibrated by the alternating electromagnetic field. Vibrating electrons emit radiation. The light is reflected. This is why metals are shiny and reflective.

Sound works differently. In air, it is a compression wave. A sound source is a vibrating surface that pushes air away and then pulls back. It creates a region where air molecules are crowded together at higher density, followed by a region where they are at lower density.
Air molecules pushed into the high density region push their neighbors forward. Those neighbors push them back. This moves the high density region forward. The high and low density regions move forward, while the atoms just vibrate back and forth.
To keep moving uniformly, the molecules in a high density region must keep pushing into molecules just like themselves. Air molecules are $O_2$ and $N_2$, fairly light. They are not strongly attached to their neighbors.
If a high density region pushes into a solid object full of heavier metal atoms, the metal atoms are not pushed as readily. The air molecules pile up and then push backwards. The sound is partially reflected. Since the metal atoms do move, some of the sound continues into the solid.
Mechanical properties like hardness, stiffness matter, but are less important. If neighboring atoms help keep a surface atom from moving, sound is better reflected.
