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I cannot distinguish and therefore mispronounce /ae/ and /a:/. Is there any different?
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It varies with the region and dialect, etc but for my midwest American English, it is the difference between cat and father.
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Hi,
they are very different. Can't you hear the difference between these two? Click on them:

/ae/ => /caet/ --- CAT
/a:/ => /ca:t/ --- COT

You can check this out too: American Vowels
That comes from this webpage http://www.americanaccent.com/pronunciation.html , which talks about some important feature of American English (it's Ann Cook's website). I don't know if you are interested in American English or British English, but I'll give those links anyway... someone might be interested.
Emotion: smile
Students: We have free audio pronunciation exercises.
Comments  
The first one appears in cat, for example, whereas the latter one is a long vowel, for example, the one in a car.
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