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I would like to open up a window in my house, let the air in, but keep the sound out. Could a device be designed to put up on the window, like a screen, and accomplish this?

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In principle one could use and array of active dampers, though I'm not certain what range of frequencies could be managed or what density of devices would be needed. – dmckee♦ May 16 '12 at 17:36

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The typical solution is what is know of as a Baffle Box. Basically, you create a crooked path for the air to flow through, with each turn insulated with sound absorbing foam.

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Never knew about this. Very nice. – Abid A May 16 '12 at 18:57
I presume that these are most effective on high frequencies, which suggest active damping for the regime below the baffle's effectiveness (low frequencies being relatively easy to manage actively). – dmckee♦ May 16 '12 at 19:08
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Using sound proofing materials like are used in low-end home recording studios would work well as the 'walls' or 'baffles' in the baffle box and thus, being much more effective at damping sound than most other materials, would also allow for fewer baffles (fewer: walls / turns / corners) making the box more compact ideally so it could sit more easily in the window without protruding in/out too much (without knowing the details of the window in question).

Example of material known as acoustic foam: http://www.amazon.com/Acoustic-Foam-1-1-24-18/dp/B0002ZPLPC/ref=sr_1_3?ie=UTF8&qid=1337188742&sr=8-3

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But would this foam let air in? I understand the application in sound proofing a room, but not sure how it would let air in through a window. – Abid A May 16 '12 at 18:58
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To clarify, you do not cover the window opening completely with a single piece of acoustic foam, you simply make a 'path' for the air that is 'indirect' wherein the 'walls' or surfaces are covered with the foam; if you were to look at the open part of the window from any direction you could not see through to the other side, but perhaps you could put your bent arm through the path in a 'U' or 'V' shaped path, or perhaps a cat could crawl through an 'S' shape, etc., for example. But all the while all you can see or feel would be foam. Did you look at the illustration in Don's link? – NOTjust -- user4304 May 17 '12 at 1:17

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