A ______ is defined as a mechanism of energy transport that moves through a substance by inducing periodic oscillations in its constituent particles.

The correct answer is wave.

A wave is defined as a disturbance or mechanism of energy transport that moves through a medium or space, transferring energy from one location to another by inducing periodic oscillations in the constituent particles of the medium without causing any permanent transport of matter.

Let us break down the terms provided in the options to understand why wave is the correct choice:
• Wave: The macroscopic phenomenon and mechanism responsible for carrying energy across distance through systemic periodic oscillations.
• Vibration: The localized back-and-forth or up-and-down oscillation of an individual particle around its equilibrium position. While vibrations of individual particles create a wave, vibration itself refers to single-particle movement rather than the overall transport mechanism across a substance.
• Wavelength: A structural parameter of a wave defined as the physical distance between two consecutive corresponding points (such as two consecutive crests or troughs). It is a property measuring distance, not a mechanism of energy transport.
• Amplitude: The maximum displacement of a vibrating particle from its rest or equilibrium position. It describes the wave's strength or energy magnitude, but is not the transport mechanism itself.

Therefore, the completed definition is: "A wave is defined as a mechanism of energy transport that moves through a substance by inducing periodic oscillations in its constituent particles."