The uniform that you describe is USN enlisted.My thoughts would be that since there is nothing on the left or right sleeve that it was taken shortly after he went into the Navy.Also with a dob 1901 it is possible that it was took durning WWI since he would be 18 by 1919 when the war was over.
I think that it is likely that it was taken between 1919 and 1931 and that he was on the USS Hart DD-110/DM-8 since the USS Hart DD-594 was commissioned in 1944 and decomed in 1946.IT did happen but it would be very unusal for a 45 year old man to be an apprentice in the 44-46 time period on DD-594. If he was petty officer or any thing other than a apprentice is rank would be on either his left or right sleeve.
Just my thoughts, I was not in the Navy at this time but later did 30+ years. Please contact me at Poindexter16@hom.com if I can be of help.