Run by a non-profit with an aim of making music freely and openly available, Musopen provides access to public domain music and allows users to upload music that is in the public domain. The site also offers access to public domain sheet music.
NASA offers a variety of audio content on SoundCloud. According to their content use page, this content is "generally not copyrighted" and may be reused.
Creative Commons Audio Content
If you aren't able to find a public domain audio clip that suits your purposes, there are also many resources available to find music and other sounds that have been licensed under a Creative Commons license. Below are some of the best of these tools.
This website makes it easy for users to upload sounds they have recorded or created and license them under a Creative Commons license. Users can choose to release their works into the public domain or select one of two Creative Commons licenses, so it is important to review the specific licensing and attribution information for each sound you plan to use.
All audio files on this site are in the public domain or licensed under a Creative Commons Attribution-Sharealike license. You can find specific information about the license attached to each piece under the link to the file.
Wikipedia provides access to a wide range of music that is either in the public domain or Creative Commons-licensed. While the site indicates that the music is "free," it is important to note that this is not synonymous with "in the Public Domain," so you will need to review the license information for the music to ensure you attribute it properly.