You could have one horn drawing exessive current. Try adjusting it. "Rig" a clip lead so you can jumper the relay coil out at the horns
The horn wiring in these cars is a little flaky. For one thing, the relay is FAR from the horns --- the wiring is not very big --- and the main high current horn power MUST PASS through the bulkhead connector, so IT can be a problem as well
Rig your voltmeter at the horns and measure voltage while honking them
IF the voltage seems low, move back to the bulkhead connector. WARNING I just looked at the 72 shop manual download, and there is a MISTAKE as to which connector the horn wire (should be dark green/ red) goes through the bulkhead
Check voltage on both sides of the bulkhead
I assume the relay plugs into the fuse box? Maybe not. You need to try to get right to the relay, and check battery voltage in "when honking" against horn voltage out. Diagram shows battery supply to the relay as H1-16V (no 16 violet goes to in harness splice)
From the relay out through the bulkhead to the horns as H2-16DGN/R (no 16 dark green / red) but the bulkhead feed is ambiguous
The "My Mopar diagrams show thus:
http://www.mymopar.com/downloads/1972/72DartA.JPG
http://www.mymopar.com/downloads/1972/72DartB.JPG
THEY ARE ALSO WRONG. They show the horn wire going to "L" in the bulkhead, which inside the car is the YELLOW start wire.
The "inside" bulkhead connector shows "T" at the bulkhead. So the start and horn wire goes to either L or T, you'll have to find out. The 74 diagram shows it going to T so I would tend to believe that.
Below are the 74 Dart diagrams which I believe correctly showing the horn wire going to "T" in the bulkhead:
http://www.mymopar.com/downloads/1974/74DartA.jpg
http://www.mymopar.com/downloads/1974/74DartB.jpg
Below are some screenshots from the 72 shop manual:
Below, you see the horns 16dgn/r going to "L" at the bulkhead. I BELIEVE this should be "T"
Below, we see the INTERIOR bulkhead, and it shows "L" being the S2-Y which is the START wire
It shows "T" being H2-16DGN/R which is horns
Below, the horn relay/ buzzer. Top right is H3-20BK which goes to the horn button. GROUND that terminal to actuate the relay
Bottom right is G2-16DGN/R which goes through the bulkhead to the horns
Left center (B) H1-16V is battery power TO the relay which comes form the "in harness splice." THIS IS NOT FUSED