Final answer:
When you hear a thumping sound while driving, it is safest to pull over and check your tires as the sound may indicate a serious issue.
Step-by-step explanation:
If you hear a thumping sound while driving, the most sensible course of action would be to pull over and check your tires. Ignoring it or merely drowning out the sound with the radio does not address the potential safety issue that the noise might represent. Speeding up to get home faster is dangerous and can exacerbate the issue if there is a real mechanical problem. Checking your tires can help you identify if there is a flat or if the tires are damaged, preventing a potential accident.