Works copyrighted before 1964 had to have the copyright renewed sometime in the 28th year. If the copyright was not renewed the work is in the public domain. It is best to search 6 months before and after the required year. Some magazines are published the month before the cover date and some registrations may be delayed for a few months.

The May 13, 1940 issue of Newsweek would have to be renewed in 1968. Online page scans of the Catalog of Copyright Entries, published by the US Copyright Office can be found here: http://onlinebooks.library.upenn.edu/cce/

The search of the Renewals for Periodicals for 1967, 1968 and 1969 show no renewal entries for this issue. John Mark Ockerbloom records no renewals before 1978 (i.e. for books published prior to 1950). The online Copyright Office database, which has entries starting in 1978, has renewals starting with Newsweek. Vol. 37, no. 2, Jan. 8, 1951 (reg. no. RE0000046287).