goodreader
User Manual
Play Audio Files in the Background

Play Audio Files in the Background

Do you want to listen to music on your iPhone / iPad while surfing the web or doing something else? The easiest way to do it is to open your audio files with the GoodReader app.
First, transfer a file to GoodReader (see: How To Import Files & Folders), then tap a file name to open it.
Upload the file you would like to listen to

Then click on the uploaded file - the audio will start playing automatically.
Next, press the Hide button – this will bring the audio player to the background.
Note: While GoodReader is capable of playing audio in the background while the device is locked, there's a vital data security consideration.

By default, GoodReader puts all its files (with some exceptions such as iCloud files) under Apple's Data Protection engine, regardless of whether or not you are using GoodReader's own file encryption. This engine makes sure that protected files are physically inaccessible while the device is locked by the device passcode. While being a nice security feature, this may prevent audio from being played while your device is locked. As a workaround, GoodReader allows you to exclude all audio files from Apple's Data Protection so they could be physically read even if the device is locked. You can find this setting in the Settings menu on the main screen of the app, in the "Security Settings" section.
Related Questions

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Outstanding pdf reader and sync tool

I had been looking for a pdf reader that would directly work with files on my NAS, setup through ownCloud since I wanted the ability to annotate pdfs both on IOS and Mac. This reader annotates and syncs to ownCloud that I can read and annotate on Mac using Adobe Acrobat. Since ownCloud works across internet, all my files are always available and synced. Adobe Acrobat falls short of this feature set as their ability to work across various networked drives is very limited.

Rpriyadarshi, Review on Apple Store