Yes! It's from musical notation. P (which stands for PIANO in Italian) = quiet/quietly, PP (pianissimo) = very quiet/very quietly, F (which stands for FORTE in Italian) = loud/loudly, FF (fortissimo) = very loud/very loudly.
Ah! Of course. (In my very limited time playing the trumpet, I didn't have much occasion for p! But our son definitely sees these playing the piano so I should have put two and two together.) Thank you!