Why do my transformers hum sometimes?

You may be experiencing a high level of root and/or residual DC offset (DC leakage) in your incoming AC thanks to our utility companies. Many of us are actually experiencing some very high levels of DC signal in our AC. Some way in excess of +/< 12Vdc. However, unless it's detected audibly or in a mechanical manner (such as in your case), it generally goes unnoticed.

Occasionally, when a distortion signature is noted in an AC sine, it is often DC leakage. So you're correct in assuming a distortion in the AC signal.

Here's another wrinkle --

In my old house, I used to get humming transformers in my audio gear. I installed dedicated 20 amp outlets and the humming went away. So, it seems that sometimes transformers hum when they don't get enough juice. Dedicated circuits might also help.

Because they don't know the words?

(Sorry, it must be Friday!)
Have a nice weekend. :-)