I assume you've seen a string instrument play, right? The pattern of motion that you see the string undergoing when it's producing sound is a standing wave. You're correct that it is a transverse wave, since the motion of the string is perpendicular (transverse) to the string itself.
Basically the way string instruments work is that when the player draws the bow across the string, the bow exerts a frictional force on the string. This pulls the part of the string that the bow is touching sideways a little bit. Then that part of the string pulls the parts adjacent to it sideways, and those parts pull the parts adjacent to them sideways, etc. etc. This is a traveling wave. (For another example, imagine - or better yet, actually try this - holding a string a few feet long and shaking it slightly side to side. You'll see a wave traveling down the string, although unless you have the string pulled tight, it won't travel very far) Now, when the wave gets to the end of the string, it can't go any further, so it bounces back. Of course, the bow is still pulling on the string this whole time, so when the wave bounces back, it meets another wave that's on its way up from where the bow is pulling the string. The two traveling waves going in opposite directions make a standing wave. For some more explanation of this, you can look at
Wikipedia.
Anyway, the net result of all this is that when you play a string instrument, it doesn't take very long at all to create a standing wave on the string. Remember, this means the string is vibrating side-to-side all the way along its length. (unless there are nodes at certain points on the string - that's something for you to look up) These vibrations cause the string to bump into air molecules, which creates pressure waves, a.k.a. sound waves, that travel through the air much the same way that the waves of vibration travel along the string (although the waves in air are longitudinal, not transverse). That's how the sound reaches people's ears.
