Add silence to the end of an MP3

With ffmpeg, you can use the aevalsrc filter to generate silence, and then in a second command use the concat protocol to combine them losslessly:

ffmpeg -filter_complex aevalsrc=0 -t 10 10SecSilence.mp3
ffmpeg -i "concat:input.mp3|10SecSilence.mp3" -c copy output.mp3

You can control the length of silence by altering -t 10 to whatever time in seconds you would prefer. Of course, you only need to generate the silence once, then you can keep the file around and use it to pad each of the files you want to. You may also want to look up the concat demuxer - it's slightly more processor-intensive, but you may find it easier to drop into a shell script.

If you want to do it in a single command, you can use the concat filter - this will require you to re-encode your audio (since filtergraphs are incompatible with -codec copy), so the option above will probably be best for you. But this may be useful for anyone working with raw PCM, looking to add silence to the end before encoding the audio:

ffmpeg -i input.mp3 \
-filter_complex 'aevalsrc=0::d=10[silence];[0:a][silence]concat=n=2:v=0:a=1[out]' \
-map [out] -c:a libmp3lame -q:a 2 output.mp3

Control the length of the silence by changing d=10 to whatever time (in seconds) you want. If you use this method, you may find this FFmpeg MP3 encoding guide useful.

You can do so easily with SoX's pad argument and the following syntax:

sox <oldfile> <newfile> pad <silence at beginning of file> <silence at end of file>

Example:

sox mp3.mp3 mp3withsilence.mp3 pad 0 1

Those silences are in seconds. (Other usages are possible using a different syntax, so as to insert those silences at specific positions. See the SoX documentation for more.)