The word "syringe" comes from syrinx. Think about it: syringes are hollow just like reeds.
Syrinx is the name of birds' voice boxes, just like the larynx is the voice box of humans and other mammals. (The reedy nymph thinks it's nice that she's the namesake for the thing that allows birds to sing their pretty songs.) (Source.)
Syrinx is also the name for a tube-like, fluid filled cavity in a person's brain or spinal cord. You don't want one of these.