Date: 201904
Local time of day: 1201-1800
Location: ZZZ.Airport, US
Flight conditions: VMC
Weather elements / visibility: 10
Light: Daylight
Aircraft: Skyhawk 172/Cutlass 172
Operator: FBO
Operating under: Part 91
Flight plan: VFR
Mission: Training
Flight phase: Final Approach
Airspace: Class G ZZZ
ATC / advisory: CTAF ZZZ
Second aircraft: Amateur/Home Built/Experimental
Reporter organization: FBO
Reporter function: Instructor; Pilot Not Flying
Reporter qualification: Flight Crew Commercial; Flight Crew Flight Instructor; Flight Crew Instrument
Human factors: Communication Breakdown; Situational Awareness
Anomaly: Conflict NMAC
Detector: Person Flight Crew
When detected: In-flight
Result: Flight Crew Took Evasive Action
Contributing factors: Human Factors
Primary problem: Human Factors

Narrative: On a last minute evening flight with a student; we encountered more than we bargained for on our routine training flight. We took off and went out to the practice area to do ground reference maneuvers. While we were out there; we heard two experimental aircraft in the same general area and heard when they switched to a private frequency (to which we placed on our second radio for monitoring purposes.) During our entire training session we were passively listening to the two experimentals out for a fun duo sightseeing flight. We made them aware of our position and the three of us stayed apart from each other. When we were done with our lesson; we headed back for the airport making all applicable position reports on the CTAF (we do not have a tower). We eventually entered the pattern and flew the downwind and base with no issue. We were still monitoring the second frequency and could hear the two aircraft were still on the other side of the mountain; roughly 9 miles away; so we considered them no factor. We did not hear anyone else on the CTAF and did not see any other traffic. We turned final for runway XX and I decided to have the student land without flaps because we had been going too fast to put the flaps down and I decided it would be a good opportunity to review landing without flaps. We approached short final at 70-80 MPH (we were in an older 172) and I was so focused on the approach and explaining the visual difference of the touchdown and how it would feel different in ground effect; I never thought to look at the final approach area of the short; rarely used crosswind runway (Runway XY). Winds were calm and we were using the designated calm wind runway. As we were about to cross the approach area of Runway 30; I saw a plane at the same altitude coming at us from the left (he appeared in the pilot side left window). I had enough time to say 'PLANE!' and push the yoke forward. We passed underneath the little experimental airplane roughly 10-15 feet. I could clearly see the plane as we went below. The ground was roughly 20-30 feet below us because after pushing underneath I felt the ground effect. We continued in ground effect and decided to abort our landing and head out to the west to figure out what was going on. At this point; I was thinking that was one of the party of two experimental aircraft that I had been monitoring on our second comm. I could not figure out how I didn't hear them return to the airport. We turned around about 8 miles away and then came back and re-entered the traffic pattern with much caution and landed safely. Upon entering the FBO; the pilot of the rogue airplane was waiting for us. He looked like he'd seen a ghost and immediately began apologizing. I asked him why he was apologizing and he said that it had been him that was landing on Runway XY; that he had been on the wrong frequency; and that he did not see us until we were underneath him. He said he had been on [a discrete frequency] instead of the CTAF. He could not believe the mistake. I could tell he was very sorry. My student and I accepted his apology and then said that we should have been looking for traffic better and we were also at fault for failing to do so. We had become so focused on the radio traffic; and had been so complacent thinking we were alone in the pattern that we never looked at the approach for that crosswind runway when we were far away from it. The other pilot said he would be much more observant when setting his radio in the future.It turned out that the two experimental aircraft we had been monitoring were in fact 9-10 miles away like they had reported; and the third aircraft had been floating around the area thinking he was broadcasting on the CTAF and we did not even know the third aircraft was in the vicinity. He had departed 5 minutes before we did; and returned at the same time. The flight lasted [one] hour. After the fiasco; I mistakenly called out one of the party planes asking him if he hadseen us as we flew underneath him. He seemed shocked and said he had not seen us. It was a case of mistaken identity. He had really not seen us because he had never come close to the airport region. His aircraft looks identical to the one we went underneath; so I made an erroneous assumption--what's that saying about making assumptions? I had to apologize to the mistaken identity pilot right after the wrong frequency pilot apologized to me. The entire scenario could have been prevented if the wrong frequency pilot had been on the correct frequency (1) and if I had been looking for aircraft that may not have radios (2).




Synopsis: C172 Instructor reported an NMAC during landing at a non-towered airport with crossing runways.