In the Audacity Tutorial you discovered the ease of Audacity to record, edit, and export your audio. But, Audacity is as powerful as it is simple to use.
I have seen many garage, Indie, and professional bands mix their work with Audacity. This is why Audacity work are called project files. In Audacity, click the drop down menu Project. From there you have the option to import other tracks from a previous recording or MIDI file. Another way to get multiple tracks in a project is to click Record like you would normally, then push stop. Pushing Record again will start another track recording.
You can also highlight a certain part of the track or all of it and click on the drop down menu Effect, there is an endless amount of things you can do to distort, modify, and change the sound.
A podcast or webcast is simply recording of a show, lecture, general audio that is not live. It is a recording saved for later. This is incredibly useful for later recall but can also be a valuable way for your students to record their learning.
Once you have your recording, click on the Project drop down menu and click Edit ID3 tags. This is the information that shows up on your computer music player (e.g. "Title: Quadratic Equations").
When studying sound waves it can be really helpful to see such an abstract concept visually. With Audacity you can record yourself singing (if you are so brave) or find all of the different pitches within a song you imported. To do this, click on Analyze and Plot Spectrum.
You could also record two different tracks with two different pitches and zoom in to see the waves created. If you would like to create a specific frequency, click on the drop down menu Generate and click on Tone. The students really enjoyed it when we discuss the Mosquito Ringtones, it really drives home the point about how our ear works and threshold of hearing. They freak out when they are unable to hear what their peers are able to.
Visual Analyzer software. It is so much fun to watch the students challenge each other to make the different frequencies and they love to see their music change the wave. For a typically invisible concept like sound and air pressure, I am grateful to both Audacity and Visual Analyzer for making their software free to all.
I would also like to recommend a blog post by a fellow #EdChat Tweeter David Wees. He had a lot of great ideas that I would recommend you take a look at.