Final answer:
The vibrating horn on a Type III hydrant system sounds when there is a drop in system pressure, which could indicate a possible leak or compromised fuel flow.
Step-by-step explanation:
The condition that will cause the vibrating horn to sound on the Type III hydrant system is a drop in system pressure. In the context of a Type III hydrant system, which is typically found at airports for fueling aircraft, the horn is a safety feature designed to alert personnel to a potential problem. Specifically, when the system pressure falls below a predetermined threshold, the drop in pressure triggers the alarm system, which includes the activation of the vibrating horn. This serves as an immediate warning that the fuel flow may be compromised or that there is a possible leak in the system. Prompt investigation and corrective action are critical to maintain safety standards and prevent any potential hazards associated with fuel mishandling.