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Then how my Galaxy S3 did not have any distortion when I applied these Apps....it had the same sound limitation like the Tab 3?
Different devices have different audio hardware. There's not really a rhyme or reason to it between devices. Its just whatever they wanted to use for audio, and different chips have different output levels. Unfortunately, sound hardware on many mobiles are highly undervalued, so many devices have very mediocre (cheap) sound hardware.
Your S3 may just have more powerful and better sound hardware than your Tab. Not really much you can do about it. Like Rukbat said, buy an external amplifier.
Because the audio amplifier in the device has a fixed amount of output. Pushing it beyond that increases distortion somewhere around exponentially. (IOW, 2X the volume, 4X the distortion. 3X the volume, 9X the distortion.) About the only real solution is an external amplified speaker. They make some pretty small Bluetooth speakers with pretty good volume.