Transmitting many wave-type signals, sound, radio waves etc, get disrupted when they meet parts of their route that have different resistances (impedance). At a point of change, part of the signal is reflected and part transmitted, depending on the relative impedance either side. The best transmission happens when there is no impedance change.
So once a sound wave is inside the solid, it transmits well as the impedance stays constant. A sound wave in air comes up against a change in impedance when it hits a solid wall. Only a small proportion proceeds forward into the solid, the larger part is reflected.
For this reason, the best sound absorbing material is a sandwich of alternating layers of stiff, dense material separated by air gaps or something like foam, so as the sound wave progresses, it comes upon multiple mismatches of impedance in its path.
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