Evidence: sound maker videos, making sound lab
The speaker and instruments moving back and forth in different patterns seems to be related to the type of sound they produce.
When an instrument vibrates (makes sounds), it includes the following actions:
A force is applied to a part of an object; that part bends or deforms and changes shape. Energy is transferred to the object.
When the force is removed, that part of the object springs back and overshoots its starting position.