What are some alternatives?
When comparing Reaper and Audacity, you can also consider the following products
LMMS - Make music with a free, cross-platform tool
Ardour - Record, edit, and mix on Linux, Mac OS X, and Windows.
FL Studio - Image-Line's FL Studio, now on it's 12th version, is a well-known music production suite and the most popular beat processor on the market, due no doubt to its longevity. Read more about FL Studio.
GarageBand - GarageBand is a fully equipped music creation studio for Mac
Ableton Live - Ableton makes Push and Live, hardware and software for music production, creation and performance. Ableton´s products are made to inspire creative music-making.
Reason - Reason is a program that you can use to create music.