I have locations of the points which produce sound. I want to create a sound map based of those points, topography, and the distance at which a sound can travel. On this picture you can see the red dot indicating the source of the sound; yellow dots indicate location which would be impacted by the the sound coming from the source; purple points indicate location where you won't hear the sound coming from the source location, because there is a major ridge blocking it. Is there a way to do this in ArcGIS?
Well, I don't know if there are any standard out of the box ArcGIS tools set up for sound modelling, and I know sound-waves do have different properties than light waves that may affect your modelling (ex: echo/reflected sound), but there are out of the box tools for modelling line of sight from given point(s) that may work for what you need.
Anyway, I would suggest reading up on the tools before just going forward with it, but the basic principle is you feed the tool an input point with specific fields containing values for maximum distance, elevation off the ground, angle, etc. and you give an input raster elevation dataset like a DEM. The result is a raster showing which spots have direct line of site with the input location given your parameters.
There may be other tools out there specific to sound modelling, but if line of sight modelling would get you close enough, looking up Viewshed analysis will get you at least pointed in the right direction.