Why use solids for soundproofing when sound waves travel through them faster? I'm doing a soundproofing experiment where I test out different materials with different specific heat capacities to see how SHC affects how much sound level is emitted. But I also know that sound travels through solids faster than liquids or gases, so theoretically would a liquid or gas be better at soundproofing since sound can't travel as fast through them? Or does the speed of sound not have any effect in how much sound we can hear?
 A: the speed of sound is unrelated to the sound-deadening characteristics of materials, except as follows: 
The speed of sound in any given material is related to the acoustic impedance of that material. When a sound wave travels from one material (like air) into another (like a 2x4 stud wall sheathed with 3/4" drywall) where the acoustic impedances of the two materials differ greatly, then the resulting impedance mismatch will cause some of the incident sound wave to be reflected off the interface and therefore not penetrate the wall. This mismatch effect is one tool used by acoustics engineers to design walls that stop the transmission of sound waves.
A: What do you mean by "sound proofing"?  Some people confuse sound proofing with reverb reduction, completely different task.
While I see you have an accepted answer I want to add something to this that I think is missing.  The goal of sound proofing a room is to control the transmission of sound both into the room from the outside and out of the room from the inside.  If one is building a recording studio you do NOT want unwanted outside noise coming in.  If you don't want your neighbors calling the police during band practice you don't want sound exiting the space into the environment.  Most materials do both at the same time.  Reducing reverb, a much need practice in almost every restaurant in America, does not require sound proofing and doesn't lead to it.
You are correct that sound typically travels faster in solids but that doesn't mean anything.  Materials have certain properties that (1) reflect sound, (2) transmit sound, and (3) Absorb sound.  Some of the hardest materials (with the highest sound speeds) are great reflectors.  All materials do these three things to some extent.  And they behave differently at different frequencies.  So your sound proofing might work well for most sound but transmit 1237Hz!  Part of this has to do with the thickness of the material.  The material will respond in such a way that for certain incident wave it is opaque and for other completely transparent.  Soft materials are good at absorbing sound which means that once the acoustic wave hits the material and travels into it the energy is converted to internal movement of the molecules and changes the thermodynamic state of the material, at least for a short time.  Such materials act as breaks for acoustics.  Again, I cannot stress this enough, there is no "perfect" material that I know of that works with the same efficiency for all audible frequencies.  Furthermore, the use of soft materials does not prevent the entire wall from being pushed back and forth by the incident sound at some frequencies and in that process creating (transmitting) sound to the outside world.
What you need is a combination of both.  Good sturdy hard layers with soft absorbing material in between.  If one assumes ideally rigid walls and building frame then creating an echo chamber might work.  But you might be surprised at how flimsy some construction is (or perhaps not since you are aware that conversations inside a room can be heard outside).  There is a construction material called baffling which I am sure you are familiar with.  Some types of baffling are for noise and reverb reduction but they actually make walls that are layers of sheet rock with absorbing material in them (or at least they used to).  I am seeing a lot of DYI stuff online for making your own and mass loaded vinyl (the miracle material).  In the old days this type of wall material weighed a ton and most places where not built to code for it.  The mass was great enough that if you hung it in place of ordinary dry wall you could see structural damage to the building frame over time.  This had to do with the spacing between wall studs and floor support beams in the original structure.  I think modern materials are much lighter.  
In any case solid does not always mean acoustics propagates through it.  Even if the local sound speed in a layer of absorbing material is high the attenuation factor might be so large that any sound that enters will die within a few millimeters, like the electrostatic field in a conductor.  
