Thank You note after private sample lesson with professor?

Is it customary for an applying student to send a short Thank You note (an actual paper one) to a college professor who gave him a private lesson on his audition day, especially if there was no charge?

A follow up note or email is always appreciated (speaking as a professor who does interviews).

My S sent emails. Some sort of thank you is completely appropriate.

My D sent emails, always. Regardless of how much or little we paid for the lesson.

My D sent an email thank you to each professor with whom she had a lesson, regardless of whether free or paid.

A written thank you note expressing gratitude is never inappropriate.

My D did written thank you notes

mine also emailed thank-you’s for sample lessons, mini lessons, meetings with AOs, etc…

Famous player and teacher at well-known school speaks to my daughter at great length about how she wants students to think for themselves, have their own ideas, etc. A few minutes later, she asks my daughter what color she believes the passage in question is.
“Blue,” my daughter offers.
“Blue?!” the teacher screams. “Noooo! And I’m going to forget you said that. What color is it?”
Rest of the lesson more of the same… “play it like this” teaching, and markedly unfriendly.
Even she received an exceedingly polite thank you email after the sample lesson.
All teachers who took the time to give my daughter a sample lesson received thank you notes.

Great story about an awful teacher. (One of my daughters has synesthesia so she would have thought that teacher was crazy.) Also, “think-for-yourself” and “play-it-like-this”–what kind of schizophrenic teaching style is that?)

Hah, GH. It would have been brutal for her. Actually, it was pretty brutal for my daughter. And that color thing was no metaphor. It’s verbatim – and there was a lot more where that came from. We laugh about it now. Just have to say that the experience underlines – in blue, or whatever color you choose – the incredible value of the sample lesson.