Who discovered the sound wave and when was that?

Pythagoras, ancient greek  philosopher and mathematician, studied the strings' vibrations, somewhere around 500 B.C.

Another greek philosopher, Aristotle, made an assumption about sounds which are moving along with air moving, reaching our ears.

In 1600's, Galileo has demonstrated that the pitch is determined by the sound waves frequency.

Again, an important discovery linked to sound waves is the phonograph, invented by Thomas Edison, in 1877.