Long-lasting intermittent "drip" sound behind/under kitche sink after use

After using our kitchen sink, and long after it seems to have drained, I am hearing a long-lasting (30 minutes) intermittent (every 10-15 seconds) dripping sound which I think is coming from behind or under our kitchen sink. This has been going on for months and I see no water damage in the wall or the finished basement below. I've read up about expansion noises when running hot water, but haven't had chance to check whether it only happens after using hot water yet. I've also read that it could be related to the P-trap if there is improper venting. I don't know much about vents. The drain appears to go directly into the wall (exterior) from the P-trap, so I can't comment on the vent.

How likely is this to be an actual leak, if we don't see water damage? I'd hate to ignore this if it's destroying the wall!

Thanks for any suggestions. I'll probably end up getting a plumber out, but I thought I'd ask here anyway.

It's hard to say,do you have an Ro system(reverse osmosis)

Ran the cold water this morning, no drip sound. So, it seems like its related to hot water (either supply or drain).

No to the RO system question.

So after a quick test it appears to happen when I run the hot water in the kitshcn sink, not the cold.

phryas said:

So after a quick test it appears to happen when I run the hot water in the kitshcn sink, not the cold.

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It's not water dripping. It's your hot line ticking. Happens more often than you would think. Means that the pipe is tight against a wood stud or block.
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SHEPLMBR said:

It's not water dripping. It's your hot line ticking. Happens more often than you would think. Means that the pipe is tight against a wood stud or block.
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Additionally, just so that you are not tricked by which pipes (water supply or drain) are expanding you should try pouring two buckets of hot water, consecutively, down the drain before running the hot water from the faucet. If you start to hear the ticking, then it may be your drain expanding. If it's quiet, run the hot water in the sink, but don't let it down the drain. fill buckets or containers and empty them elsewhere and after a while shut off the water and listen.
This process should narrow down what the cause could be.