[ðiː] - when the speaker emphasizes it, to mean "the very ...". It is stressed and prolonged. [ðə] - normal case, when "the" comes before consonants: "the night", "the work", ... [ðɪ] - normal case, when "the" comes before vowels: "the ocean", "the artist", ...

ðə stʌdi əv spiʧ saʊndz

barely noticed

Tony gave a good explanation, but keep in mind that those are not hard-and-fast rules. In informal speech it's common for people to always say /ðə/ and in very formal speech people people might always say /ðɪ/ if they're trying overly hard to speak clearly, but in reality it's somewhere in-between. The 'rule' that you should say /ðɪ/ before vowels and /ðə/ before consonants is a very good one to follow if you want to sound the most natural, but it doesn't need to be strictly adhered to and you'll hear native speakers break the 'rules' on a whim. In general you'll sound more natural if you follow Tony's advice, but if you say the 'wrong' one it's not a big deal, and native speakers might not even notice.