What is the /ū/ sound in English symbol?

In the American Accent Training, it shows /ū/ (a line over u) is a tense vowel, and takes "smooth" as an example.

However, according to Merriam-Webster dictionary, it should be [ˈsmüt͟h], and there is no any /ū/.

What is /ū/ on earth?

Solution 1:

Different publications use different conventions. If said book uses "ū" to mean the vowel in smooth, i.e. /uː/ or /u/ in IPA-based conventions, and \ü\ in Merriam-Webster, then it is. You can never expect a symbol in one source to represent the same thing in another.

Traditionally, though, "a", "e", "i", "o", or "u" with a macron above it meant "the sound of the name of the letter" in dictionaries from the 18th and 19th centuries. So "ū" in those old dictionaries corresponds to /juː/ or /ju/ in modern IPA conventions, and \yü\ in Merriam-Webster. But not "ū" in your book.