This 2015 TED-Ed lesson, written by Oscar Fernando Perez and animated by Chris Boyle, walks through what happens when a guitar string is plucked: the string vibrates in a set of standing-wave modes, the fret and tension set the pitch, and the body resonates to make it audible. It is aimed at school-age viewers and the full lesson with questions is on the TED-Ed site.
It is here as background rather than as cymatics. A Chladni plate is a string's standing waves in two dimensions, and a dish of water is the same idea with a free surface. Someone who has understood harmonics on a string is most of the way to understanding nodal lines on a plate.
Short, clear and safe to send to anyone who asks what a standing wave is.