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I wanted to learn more about phonetics and I stumbled across this website:
http://www.oxfordlearnersdictionaries.com/us/about/english/pronunciation_english
However, I couldn't get what the difference is between the pronunciation of /i/ in the word happy /ˈhæpi/ and /ɪ/ in sit /sɪt/ and also between /ʊ/ in the word put /pʊt/ and /u/ in the word actual /ˈæktʃuəl/. This strangely only appears in the online Oxford and Cambridge dictionaries, and I couldn't seem to find it in any other.
As shown there, the vowel at the end of happy /ˈhæpi/ is what we call the FLEECE vowel. It is a tense vowel, sometimes called the close front unrounded vowel. The vowel in sit /sɪt/ is the corresponding lax vowel, the one that we call the KIT vowel, or sometimes the near-close near-front unrounded vowel.
The difference between your other pair is again that of tense /u/ for the GOOSE vowel versus lax /ʊ/ for the FOOT vowel.
You need to learn to hear the difference between these tense/lax vowel pairs, because hearing the tense–lax distinction is critical to understanding English. Until you can hear it, English will always sound confusing to you.
Here's the chart for all twelve simple vowels (monophthongs) of American English:
Notice how there are contrasting pairs of vowels:
In materials for young children, the tense vowels are often called “long” and the lax ones “short”, but this is not a good way to talk about them because vowel length is not phonemic. Plus if you were talking about length, you would have to mention that all three phonemic diphthongs (/aʊ/, /aɪ/ and /ɔɪ/) take longer to say, too.
All that said, the word happy does not always end with a tense vowel in all speakers. In those with happy tensing, it does, but in others it does not. Happy tensing is the more common variety.
There doesn't have to be a difference. It's perfectly fine to use the "sit" vowel in "happy", and the "put" vowel in "actual".
The reason Oxford dictionaries use a different transcription is simply to account for multiple accents. In some accents, "happy" instead has the vowel sound of "fleece", and "actual" has the vowel sound of "goose". This is called "happy-tensing"; it occurs for nearly all North American and Australian speakers, and for a number of British English speakers.
This may be a little confusing, but in fact it's good news for a learner: you don't have to worry about differentiating /iː/ and /ɪ/ in words like "happy", unlike "sheet" and "shit" or "beach" and "bitch". You can use whichever vowel sound is easier for you to pronounce in words like "happy" and "actual" (although as I mentioned earlier, most North American speakers are more accustomed to using and hearing the "fleece" and "goose" vowels in words like this).
