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I would assume that different materials absorb sound differently (maybe not?)

What is this called?

How can I compare the sound absorbent properties of different materials with the same surface geometry, such as plaster and gypsum board?

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What you're looking for is called the Acoustic Absorption Coefficient. Which is a measure of how much sound a material absorbs. Unfortunately, it's not as simple as that, mostly because the coefficient is dependent on frequency meaning that it will absorb some frequencies better than others. It's also dependent on the angle of incidence. Google will bring up a variety of tables, but use these with caution.

Keep in mind as well that when sound is incident upon a surface, a portion is reflected, a portion is absorbed and a portion is transmitted. Since part of the sound is transmitted, it's not just the material in question that's important, but the material behind it as well. As with the absorption, reflection and transmission are dependent upon both frequency and angle of incidence.

Any tabulated data of absorption coefficients for different materials has to be taken with a huge grain of salt and an understanding of what those numbers are and how they were measured.

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