As the Google Audio Player gadget is no longer available, I had to find an alternative gadget to use. This website has proved extremely useful and in order to use the gadget, insert it by URL from:
Importantly, the .wav or .mp3 files that you are wanting to embed on your site must be uploaded to your site first. You can do this by uploading the file(s) as an attachment to any page or by using a "Filing Cabinet" page which is what I've chosen to do. All my .mp3 files have been uploaded to this File Cabinet page (use the Add File option, not Add from Google Drive) and then embedded into my site.
This screen casting steps through the process using the File Cabinet page method.