Great question — answering as the UphillTech team:
Your tyre has lost most of its air, and is about at room pressure which is about 15 psi. This is not enough to maintain the tyre's shape against the weight of the bike, so has compressed at the bottom. When you squash the tyre with your hand, it moves air around, and this is what you're hearing. That air is either moving within the tyre or coming out through a significant hole, and then the carcass of the tyre is reestablishing its shape and the air moves back. Long story short, you probably have a failed tube. Either the valve has failed, popped out of the rubber, or some other hole has appeared in the rubber. Solution, drop the wheel, and remove tyre from rim. Extract tube from rim and...
Full answer by Criggie: https://bicycles.stackexchange.com/a/100674 (CC BY-SA 4.0).
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