That's true. The general rule is if a word starts with a vowel sound (a, i, e, o, u) then "an" is used instead of "a". That includes words like "hour" where the H is not pronounced so the first letter spoken is the O. So we say "an hour".

At AN alarming rate, because alarming begins with a vowel (a). When the word following "a" here begins with a vowel (or a silent H, as in the word "hour"), an is used instead of a.

at an alarming rate because the first letter of “alarm” is a vowel letter and the pronunciation is vowel ，too. so we use “an ” here。

"at an alarming rate" is right because any Word started with ( a - i - o - e - u ) take ( an ) .

Anytime the word following the 'a' has the sound of a vowel, you should use 'an'. Like some people said before, even if the h is silent in hour. The same rule applies to honest and heir. Believe it or not, 'an' should also be used before acronyms that start with a "vowel sound". For example, if you said, "A sport utility vehicle just passed us." using the acronym for sport utility vehicle, you'd say, "An SUV just passed us." because SUV sounds like 'ess-you-vee'. Also, when I was young, I didn't understand when I was taught to say "the vowels are a, e, i, o, u, and sometimes y". When used in the word "play", 'y' is a vowel. When used in the word "yellow", 'y' is a consonant. So you should say, "I can see a yellow bird" instead of "I can see an yellow bird."