World War I officially began for the United States on April 6, 1917, when the U.S. declared war on Germany. On May 18, Congress passed the Selective Service Act which required all men between the ages of 21 and 30 to register for the draft. Armstrong turned this requirement into a patriotic celebration by organizing a registration parade that was held on June 16.
The centennial history of Armstrong identifies the bandsmen as (L-R) "George Beck, Bill Ridley, Fred Goodge, Bert Bosworth, Lester Mason... , Vern Mitchell [trombone]... , -- Noward, Bill Brown, DeWitt Grussing (or Harry Bosworth), Tom Goodge (snare drum)." The centennial history includes another picture of the band taken in 1917 in which Bill Ridley (second bandsmen from the left above) is identified as the director of the band.
Source: Remembering Armstrong, A Centennial History of Armstrong, Emmet County, Iowa - 1893-1993, by Jo Ellen Ashmore (1992)
One fun feature of the panoramic image above is all of the children who can be seen peering around the draft registrees while the picture was being taken.