I noticed that after a transmission ends, it takes a few seconds for the 'thump' to resume.
Are you actually scanning more than one channel, or do you have it locked onto a single frequency?
Sound cards will magnify a lot of noises you probably wouldn't hear if you were listening to the scanner's internal speaker.
If possible, try to use the very minimum gain on either the MIC or LINE-IN settings in your mixer, and adjust your scanner's audio for proper levels.
Some noises, such as an AC hum remain at the same level at the scanner's speaker no matter where the volume control is set, so a low scanner volume setting combined with a high MIC or LINE-IN mixer setting will result in an amplification of the AC hum.
The fix would be to raise the scanner volume, and lower either the MIC or LINE-IN mixer setting.
If the resulting audio is too hot, you may need to switch from the MIC jack to the LINE-IN jack on the sound card.
Good Luck.