In the recently published The Dead Sea Scrolls and the Bible, James VanderKam suggests some interesting possible parallels between Jubilees-Qumran tradition and Acts 1–2. After a lengthy discussion VanderKam offers the following summary.
"Summing up, there is little in Acts 2 that recalls explicitly what the scriptures say about the festival of Weeks, but sundry kinds of evidence indicate that, in writing his account, the author drew upon exegetical traditions that had accumulated around the festival in some Jewish circles, including especially ones attested in Qumran texts.a. The Jubilees-Qumran tradition shows that by the second pre-Christian century the festival of Weeks was intimately associated with the Sinai stories from Exodus, especially with the covenant between God and Israel. The festival of Weeks was the occasion for making and remembering the biblical covenants and for renewing the great pact made at the mountain.
b. Acts 1 uses language for Jesus’ ascension that reminds one of Moses’ ascent of Mount Sinai to receive the Torah and make the covenant.
c. Summaries of the ideal fellowship in the scrolls and Acts 2:42-47; 4:32 (cf. 1:14) are modeled on the notion that Israel at Sinai was harmonious, a people that accepted the Torah without dissent and lacked the defects that otherwise disrupt society. Exodus implies as much, and later sources expanded upon the theme.
There are, of course, important differences between the Sinai stories as read in some Jewish sources and the account in Acts 1–2. So, for instance, the gift at Sinai was the divine word, the Torah, while in Acts 2 it was the divine Spirit.
Not all of the elements in Acts 1–2 arose from Jewish elaborations on the Sinai chapters. There are unique elements in the New Testament account, and it is possible that other scriptural material, as later understood, contributed to the shaping of Acts 1–2. But the evidence demonstrates that in Acts 1–2 the writer was heavily influenced by Jewish traditions about the festival of Weeks, prominently including ones known from the Dead Sea Scrolls."
James C. VanderKam, The Dead Sea Scrolls and the Bible (Grand Rapids:Eerdmans, 2012), 155-56.