Dear Mr. Gray,
Thank you for posting your request on History Hub!
We searched the National Archives Catalog and located the series titled Sound Recordings Relating to World War II, 1942 - 1945 in the Records of the Office of War Information (Record Group 208) that includes the item Description of President Franklin D. Roosevelt's Funeral Train and Procession. This sound recording captures a National Broadcasting Company (NBC) correspondent's report of the arrival of President Franklin D. Roosevelt's funeral train at Union Station, Washington, DC, and the procession from Union Plaza down Pennsylvania Avenue to the White House. It has been digitized and is available online through the Catalog as four mp3 files that can be streamed online as well as downloaded. This recording is also available through the Internet Archive, which is a private non-profit organization unaffiliated with the National Archives. Please note that this is only the NBC network coverage of the event. It is likely that there was coverage by other networks as well as local stations which were not included in this series.
In regards to finding records of a 1975 public radio broadcast for the DC Metropolitan Area, we suggest contacting radio station WAMU. You also may wish to contact the American Archive of Public Broadcasting.
We hope this information is helpful. Best of luck with your research!