B737 Captain reported the flight and cabin crews heard a loud sound during departure climb which they determined to likely be an air leak. Flight crew diverted and completed a safe overweight landing.

Narrative

Departing ZZZ for ZZZ1 at about 13;700 feet we got a very loud sound like an air horn. It sounded as though it was on the First Officers side. I would compare it to someone holding down an air horn; like you'd find at a sports event. We both agreed immediately there must be some kind of air leak or faulty seal. We immediately requested a descent to 10;000. I told the First Officer his aircraft; his radios; tell them we want to return to ZZZ. I called the cabin who said they heard it as well; they thought it was an alarm going off; and was loud enough it could be heard significantly far back in the cabin. I explained though loud and unsettling; it was minor; we already where reaching an altitude where pressurization was no longer needed and due to the issue we would return to ZZZ for a precautionary landing; I'd call them back once we caught up. I made a calm similar pa to the passengers. I heard the First Officer at this time change frequency and the Controller asked if we were [requesting priority handling]; I told the First Officer that sounds good. I considered how it was difficult to communicate; and that we would be over weight when landing and could not logically think of any reason not to. I then called ZZZ ops and Maintenance and spoke to Maintenance; they asked if we could go to ZZZ2; i said no; it wasn't suitable; and said I was ok with ZZZ3 or ZZZ. The noise made communication difficult; thus I elected calling on the radio vs crew phone. I also sent an ACARS message and ACARS diversion report. The First Officer got us on a delay vector and down to 7000. ZZZ Maintenance called Maintenance Control and Operations Control I believe and told us ZZZ was ok but if I do get time call Operations Control to verify the best airport operationally. At this time we leveled at 7000 and the noise finally stopped. I told ZZZ that id call Operations Control. I called dispatch on the crew phone; they also requested ZZZ2; i told them unable; in which the dispatcher asked if I would go to ZZZ3. I said ZZZ3 was good; it has a longer runway than ZZZ anyway; and confirmed the company would prefer I go to ZZZ3 vs ZZZ; he confirmed and acar us the new information. We informed atc; we requested the longest suitable runway; which was XXL and was in use. We requested to have fire rescue meet us upon landing. We continued the delay vectors a few more times as we ran the non routine landing check list; and overweight landing check list. Followed by setting up and briefing the approach. We then ran the descent and before landing check list. During this I briefed the flight attendants again about the precautionary landing and made a calm reassuring brief pa to the passengers. I then took back the aircraft from the First Officer. We did the rnav XXL and we landed uneventfully on XXL; exited; followed the correct flow; passengers; inspection; and proceeded uneventfully to the Gate; in which maintenance met the aircraft.I believe our training worked very well and it felt like a good sim session. We communicated well in the flight deck; even with the barriers of a very loud noise. First Officer was very quick to identify we should descend right away to 10;000. We ran the Threat and Error Management model and both briefed each other well and checked in that we were performing normally. First Officer was an absolute asset and monumental in a safe; calm; correct outcome.