Wave Properties and Models

Objective: Distinguish the motion of a disturbance from bulk transport of matter.

A wave is a propagating disturbance that transfers energy and momentum through a medium or, for electromagnetic waves, through space. In a mechanical wave, particles of the medium oscillate about equilibrium while the disturbance travels; the particles do not usually travel with the wave over the full path. Transverse and longitudinal describe displacement relative to propagation direction in ideal examples. A rope pulse can be transverse, while sound in air is predominantly longitudinal. A single pulse and a repeating periodic wave differ, and many real waves have more complicated polarization or mixed motion. A model should identify the medium or field, direction, and quantity that oscillates.

Objective: Calculate wave quantities with proper units.

Wavelength λ is spatial separation between equivalent neighboring points of a periodic wave, measured in meters. Frequency f counts cycles per second in hertz (Hz = s⁻¹), and period T is time per cycle, T = 1/f. Amplitude is the maximum displacement or change in the modeled oscillating quantity relative to equilibrium; its unit depends on what oscillates. For a periodic wave of fixed speed v, v = fλ. A 4 Hz wave with wavelength 2 m moves at 8 m/s. Frequency is set by the source in many boundary transitions while wavelength can change with speed. Amplitude and frequency describe different features; doubling amplitude does not automatically double frequency.

Objective: Explain boundary behavior and superposition.

At a boundary, wave energy can be reflected, transmitted, and absorbed in proportions dependent on the materials and wave type. Superposition states that overlapping wave displacements add; in-phase waves can interfere constructively and out-of-phase waves destructively. Destructive interference can reduce local amplitude without destroying total energy; energy is redistributed in space and time. A standing-wave pattern can form from overlapping waves traveling in opposite directions under suitable boundary conditions, with nodes of small amplitude. The speed and wavelength of a transmitted wave may differ across media, while frequency often remains set by the source. Diagrams should distinguish rays or fronts from actual material paths.