Are solids with the same density as air possible?

Question

I was recently considering how to keep a super cheap ultrasonic range sensor safe from balls (or blocks, or whatever) going down ramps (or otherwise moving at high speeds) in a physics lab. It struck me that, if there were some solid that had a density identical to air, you could place a plate of it in front of the sensor to protect it, and it would not interfere with the sensor's measurements at all. Is such a solid possible?*

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*I could, of course, use a laser range sensor and aim it through a slit... or tie a string to the ball, place my sensor farther away, use a sturdier sensor, send objects at it at lower speeds, put some sort of wire in front of the sensor close enough that it wouldn't be detected, etc. etc. etc. The real-life solutions to my problem are numerous: I'm asking about the crazy question that the problem prompted me to ask.

Answer 1

It's not just the density of the material that would matter, but the acoustic impedance. To transmit sound waves without reflection, you would need a material with an acoustic impedance equal to that of air.

The acoustic impedance $z$ of a material is given by $z = \rho c$, where $\rho$ is the density of the material and $c$ is its speed of sound. This means that your hypothetical material doesn't necessarily have to have the same density as air, so long as the product $\rho c$ is the same. The problem is that most solids have a speed of sound much higher than that of air, and for such a medium, you would need a material that's lighter than air in order to get the same acoustic impedance.

This 2016 question asked about whether such materials exist, and open-celled elastic rubber foam was suggested. That said, acoustic impedance is often frequency-dependent, and a material that would work for audible frequencies might not work for ultrasound (or vice versa.)

Answer 2

What makes gas distinct from liquids and solids is that its atoms are so far from each other, that the interactions between them are negligible. We speak here about hundreds or thousands of atomic sizes. In solids the distances between atoms are of the order of the atomic size. Thus, what we want is a solid which has the density of atoms from million to billion times higher than a typical gas, but the mass of atoms millions/billions times lower, so that the mass density is comparable to the density of the air. As air is made of oxygen and nitrogen, which are respectively 16 and 14 times heavier than hydrogen (the lightest element), such solid is impossible.

For comparison, the density of air is $1.225kg/m^3$, whereas the density of solid hydrogen is $0.086g/cm^3=86 kg/m^3$ (Please check my conversion.)

Update
According to my brief google search (see also this post) the distance between molecules in air is about $3nm$, that is about 10-30 times the size of a molecule. That is we would need molecules/atoms 1000 times lighter than oxygen and nitrogen.

Answer 3

Density is a measure of mass per unit volume. Solids, by definition, have closely packed particles, resulting in a much higher density than gases. Air, as a gas, has widely spaced molecules, leading to its low density. Air has an average density of about 1.225 kg/m³ at sea level and room temperature. For a material to be solid and have this density, it would have to have an extremely low atomic or molecular mass and very loosely packed atoms, which contradicts the structural requirements for a solid.

also, The chemical bonds that hold solid materials together require a certain amount of energy and interaction between atoms or molecules. In gases like air, these interactions are minimal, so air expands to fill its container and has a low density.

That's why they are impossible

Answer 4

You could try making a solid foam like expanded polystyrene with closed cells and fill the cells with hydrogen or helium during the production process. I think the closed cells would have to be fairly large to achieve an overall density similar to air. The problem here is the density is not uniform due to the pockets of gas and solid intercellur walls, so it might not work as a solid that is uniformly transparent to the sound. Anyway, it would be cool to have to have such a solid foam that floats around in air.