styrofoam will do absolutely nothing to muffle the sound. You need mass to absorb the vibrations of he lower frequency vibrations (bass) and/or some absorptive material for the higher frequencies. The best way would be to build a little box around your tub and pack sand around it. That can get messy. Rockwool inslulation around the tub could also be used. get the 1 1/2" or 2" sheets and tape it up good. Rockwool is VERY itchy and quite bad in your lungs. You can get rock wool sheets from industrial HVAC suppliers and what not. You could go super cheap by stuffing allot of heavy towels and old clothes around and under the tub as well. If however your tub is on a concrete floor you will loose the cooling benefits.