Foams block sound because of the way liquid is distributed throughout them – the large but thin film of the bubbles and the narrower but more voluminous channels that support the bubbles. Sound is just the vibration of molecules, and it turns out that at the frequencies we tend to hear best at, the sound transferring from the air causes the bubbles to vibrate in the *opposite* way it affects the channels, meaning they cancel each other out. Thus we don’t hear anything.
[Source for those interested.](https://www.sciencedaily.com/releases/2014/04/140424102254.htm)
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