The city recently awarded a $743,000 contract to Target Construction LLC of Salem, N.H., to build a multipurpose athletic field on a portion of Whispering Hills, the 74.4-acre site west of Cambridge Road that Woburn purchased from Northeastern University in 2010. The construction got underway earlier this month and is scheduled for completion on May 15, according to Edmund Tarallo, the city’s planning director. Woburn paid $6.7 million for the land, with the help of a $500,000 state grant. The city received a second $500,000 state grant in 2011, which it plans to use together with $370,000 authorized by the City Council for the field project. Tarallo said that once the construction is complete, it will be up to the Conservation Commission to determine when the field is ready for use.