Ask students to stand in a wide circle around you, or stand in a clearing in the centre of the classroom.

Turn on the tone generator (e.g. an application on your phone), set to about 550Hz, and check that students can hear it.

Put the phone in the bag.
Tie the string around the handles.
Spin around your head (letting out the string longer as you speed up).
Make sure everyone is silent so that students can hear the tone of the note getting higher and lower as it respectively comes towards and away from them.

Explain that this change in frequency of a sound is called the Doppler effect.
It is happening because as the note of the sound is because of how close the waves are together. Closer waves have a higher note and waves spaced further apart have a lower note.

When the source of the sound is moving towards you, the source catches up with the sound wave that was just emitted, so that the next wave is a little closer to the preceding one. Hence when the waves reach our ear from a source coming towards us, they are all closer together and sound higher.
When the source of the sound is moving away, the waves are emitted from a further and further distance away, so the waves are spaced further apart, hence sound lower.

Also heard with a car horn on while driving by. Find on youtube e.g. hear a car horn passing at https://www.youtube.com/watch?v=a3RfULw7aAY