What to Consider
Typically when thinking about acoustics, the first thought is absorptive surfaces that capture the sound so it doesn't bounce around the room. The reality is that depending on the application, different treatments and factors need to be considered. In a classroom or lecture hall, you want to increase the clarity of the speaker, while decreasing the noise from the crowd, HVAC systems, outside noises, etc... On the other hand, in swimming pools and gymnasiums, you want a lot more absorption of sound to eliminate echoes.
Remember, it is always easier to consult with an Acoustic Professional early on in the process of designing a space, rather than after it has been built, when the budget is gone, and the client is raising concerns.
The Basics of Acoustic Panels
When sound reaches an acoustic material, such as fiberglass, mineral fiber, rockwool, etc..., the idea is for the material to capture the sound rather than reflect it back into the room. Different materials have advantages and disadvantages, such as cost, performance, and appropriateness for certain environments.
The Basics of Acoustic Fabric
A fabric's job on an acoustic panel is to not absorb sound itself, but to allow sound-absorbing products behind the fabric to do their best work. The fabric should never reflect the sound before it can travel to the absorbing product. All surfaces, fabrics included, reflect sound waves to some extent. The least reflective products do the best work as finishes for acoustic applications.
It is important when designing an acoustically sensitive space to not think of acoustics as an after thought. All of the materials in a room will affect the acoustic properties of a space, from the flooring, walls and ceiling to the furnishings. And, it's probably best to get a professional involved, but, armed with some of the knowledge above, hopefully you have a better understanding of the basics.