Welcome to the Forum. No worry about the wrong Forum Section- we give all new members a couple of mistakes before punitive action is taken.
The revolver you describe would be known as a 38 Hand Ejector, Military & Police, 4th Change. This particular model started in 1905 and was called the Model 1905 until into the teens. The 4th Change was made from 1915 to 1942, with almost half million made. I find information that leads me to believe that this revolver was shipped from the factory in 1928 or 1929, but the revolvers did not go out the door in serial number order. Your grandfather's revolver could have been in the back of the bin for some time, so ship dates could vary a couple years one way or the other.
It is great that your wife's grandfather was a policeman at the very onset of the Great Depression and that the revolver is still in the family. There were probably many stories to be told if that gun could talk.