Which instrument assists with navigation utilizing radio waves?

The VOR, or VHF Omnidirectional Range, is the instrument that assists with navigation utilizing radio waves. It works by emitting radio signals from ground-based stations, which pilots use to determine their aircraft's position and stay on course. By tuning into the specific frequency of a VOR station, pilots can receive these signals, allowing them to establish their heading in relation to the station and navigate accurately along designated flight paths. This ability to provide real-time navigational information makes the VOR an essential tool for pilots, especially in instrument flying conditions.

The other instruments listed serve different functions: the variometer measures vertical speed, indicating how quickly an aircraft is ascending or descending; the airspeed indicator measures the aircraft's speed through the air; and the gyrocompass provides directional information based on gyroscopic principles rather than radio signals. Thus, the unique functionality of the VOR in navigation distinguishes it as the correct answer in this context.