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If sound travels better through denser material, why does the sound travel better without a dense wall?

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The problem is acoustic impedance matching at the interface between the air and the wall. There an analogue of Fresnel's equations dictates how much power goes into the reflected and transmitted waves, and not surprisingly the more dissimilar the materials are the more power goes into the reflected wave. You can evade this by putting the speaker directly on the wall, effectively changing the problem so that the impedance matching is now between the source and the wall.

For a slightly surprising take on acoustic impedance, see this WP article.

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