In "Word Focus" Danny McCain writes concerning Psalm 40:1:
The expression waited patiently is literally “waited, waited.” The repetition of the verb is a Hebrew idiom used to stress the action of the verb. The phrase could be translated, “I simply waited; I did nothing but wait” (Joseph Alexander, The Psalms). The point that the psalmist was making was that he remembered spending a lot of time waiting. As one reads through the Psalms, he is impressed that other psalmists did a lot of waiting, too. They mentioned this because they were probably impatient.
Source: Studies in the Psalms: Adult Teacher's Insights, page 34.