Most likely Firefox is having trouble decoding the Mp3 file that contains your recording.
Try the following;
Steps to Resolve playing audio issue in FF browser:
1. Open FF and type “about:config” in the address bar
2. Search for "media.windows-media-foundation.enabled” double click on it set it as “false”
3. Search for "media.directshow.enabled” double click on it set it as “false”
3. Close the FF browser and open again”
4. Browser will prompt to install “Adobe Flash player” follow it and install flash player