I'm hedging a little bit here. The New Adventures of Sherlock Holmes was one of a number of Holmes radio shows in the past. At times during its run from October 2, 1939 to July 7, 1949 the show dropped the first four words of the title and was aired simply as Sherlock Holmes. Information about the show is contradictary. For example one source gives the actors in this episode as Luis [Louis] Hector as Holmes (Hector also played Moriaty in several of the Holmes films) and Harry West as Watson; the actors, however, are clearly Tom Conway and Nigel Bruce. Other sources state that the show ended in 1950.
Each episode of the show had its narrator, "Joseph Bell" (the name of the Scottish surgeon who was Conan Doyle's inspiration for the Sherlock Holmes character), stopping by the home of the retired Dr. Watson, who would then relate that week's tale from his memories of the past. (Evidently Watson retired to California.) Nigel Bruce as Watson was also top billing, probably because of the show's format. Joseph Bell may or may not have been the true name of the actor who narrated the show.
Tom McKnight produced this episode. I don't know who wrote it, but this was aired during the Dennis Green-Anthony Boucher era. The story itself was suggested by an incident mentioned in "The Final Problem."
"The Haunted Bagpipes" aired on October 29, 1946 as a Halloween program.