Vacuum Stopping Sound?

We have read that sound does not propagate through a vacuum, but the articles did not specify the type of vacuum e.g. "perfect vacuum", "low vacuum"... required.Ideally, we are looking for a formula to determine if a "low vacuum"-filled material would provide effective (practical) sound damping / sound isolation. Presently, the micro-sized spheres we plan to use contain a 1/3 atmosphere, ~253 torr. If sufficient, we plan to create a thin film, a multi-layer (2 to 3) of microspheres sandwiched between two protective films as our submission for a student innovation competition. Thank you for your time & consideration.Sincerely, JS (Vancouver, CANADA)
- Jenah Sigurdson (age 22)
Vancouver, BC Canada

You're very perceptive to note that in a real, imperfect vacuum there will still be sound propagation. For ordinary air at a given temperature, the sound speed will be the same in the partial vacuum as in the atmosphere. So how does the standard demonstration in which you can't hear a bell ringing in a partial vacuum work?

The key is that sound partly reflects when it goes from one medium to another, the same way light partly reflects as it goes from air to glass.  The better the vacuum, the more different that medium is from the atmosphere and the bigger the reflection. If you imagine (unrealistically!) that the atmosphere and the vacuum are simply next to each other with no other barrier, you can calculate the reflection and transmission coefficients following the formulas on this nice site:
. For 1/3 atmosphere, you get 1/4 transmission, i.e. 1/4 of the energy propagates through. That's not great. You'd need a better vacuum to get good isolation.

What happens in a real case where you need some sort of barrier between the atmosphere and the vacuum in order to keep a vacuum? For a moderately good vacuum (say under 100 mTorr), the acoustic impedance of the vacuum and the atmosphere are so different that the barrier material can't come close to matching each, so the sound isolation should be ok.

It's hard to know how your microspheres will behave without knowing more about them. The sound your interested in probably has wavelengths much larger than the spheres. From the sound's point of view, the spheres aren't partial vacuums but just some material whose acoustic properties come from the walls and a little from the vacuum. My guess is that they won't act much differently than a thin layer of other slightly spongy material, so they probably won't do a great job. But that's a guess- experiment will give an answer.

Mike W.

(published on 04/21/2015)