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Cement board has a higher density than 5/8 drywall. It also probably, and this is just a guess, probably has a lower resonance as well (being cement), so less sound should get through.

5/8" drywall is about 2.2lb per sqft.
1/2" cement board is 2.355 lbs per sqft.

The price is comparable between the two, with cement board being a little more expensive but not by much. 1/2" cement board comes in 3' x 5' sheets, at about $10 each (about 67 cents per sqft). 5/8" drywall comes in 4' x 8' sheets at about $15 each (about 47 cents per sqft).

Is 1/2" cement board a better soundproofing material than 5/8" drywall?

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    "Cement board has a higher density than 5/8 drywall. It also probably, and this is just a guess, probably has a lower resonance as well (being cement), so less sound should get through." Water has a lower density than air but it transmits sound better than air. Insulation is less dense than drywall and transmits less sound. It's not how dense it is but rather how well the material transmits vibration. – JimmyJames Jan 23 at 18:10
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