Periodic Motion: Amplitude, Frequency, Phase & Wave Types

Periodic Motion

Periodic motion is motion that repeats itself at regular time intervals — a pendulum swinging, a mass bobbing on a spring, a vibrating guitar string, or the rhythmic contraction of cardiac muscle. The MCAT describes periodic motion using three quantities: amplitude, frequency (or period), and phase. These same three quantities reappear, largely unchanged in meaning, when this guide later covers sound waves and the electromagnetic spectrum — mastering them here pays off across the rest of the physics content.

Amplitude

Amplitude (A) is the maximum displacement of an oscillating object or wave from its equilibrium (rest) position. For a mass oscillating on a spring, amplitude is the farthest distance it travels from the spring's natural length. Amplitude determines the energy of the oscillation but, for an ideal simple harmonic oscillator, not its frequency: a spring released from a small displacement and the same spring released from a larger displacement both complete a full cycle in the same amount of time — only the second traces out a bigger swing. For a wave, amplitude corresponds to intensity: for sound, larger amplitude means greater loudness, and for light, larger amplitude means greater brightness, concepts developed further later in this guide.

Frequency and Period

Frequency (f) is the number of complete cycles occurring per unit time, measured in hertz (Hz), where 1 Hz = 1 cycle/second. Period (T) is the time required to complete one full cycle, measured in seconds, and is the reciprocal of frequency:

f = 1/T and T = 1/f

A pendulum that completes 2 full swings every second has a frequency of 2 Hz and a period of 0.5 s. A resting heart rate of 60 beats per minute is 1 beat per second, so the cardiac cycle period is about 1 s and the frequency is about 1 Hz. Respiratory rates near 12 breaths per minute correspond to f = 12/60 = 0.2 Hz and T = 5 s — useful anchors when a passage graphs oscillatory physiological signals.

Phase

Phase describes where an oscillating object or wave is within its repeating cycle at a given moment, relative to a defined reference point, often expressed as an angle (in degrees or radians) or as a fraction of a full cycle. Two oscillators with the same amplitude and frequency but different starting points in their cycle are "out of phase." When two waves are aligned crest-to-crest and trough-to-trough, they are in phase (phase difference of 0°), and they combine to reinforce each other (constructive interference). When one wave's crest aligns with the other's trough (a phase difference of 180°), the waves are completely out of phase, and they can cancel each other (destructive interference) — a principle this guide revisits when covering sound and light interference.

Transverse vs. Longitudinal Waves

Mechanical waves transport energy through a medium via oscillation, and the MCAT distinguishes two types based on the relationship between the direction particles oscillate and the direction the wave travels.

In a transverse wave, you can identify crests (maximum positive displacement) and troughs (maximum negative displacement). In a longitudinal wave, the medium alternates between regions of compression (particles bunched close together, higher pressure and density) and rarefaction (particles spread apart, lower pressure and density) — these play the same structural role as crests and troughs when you later analyze pressure-versus-position graphs of sound waves.

Electromagnetic waves (including light) are transverse even in vacuum because the oscillating electric and magnetic fields are perpendicular to the direction of energy transport. Sound cannot travel through vacuum because it requires a material medium to sustain compressions and rarefactions — a high-yield contrast for multi-discipline passages.

Wavelength and Propagation Speed

Wavelength (λ), measured in meters, is the distance between two consecutive identical points on a wave — crest to crest, or compression to compression. Wavelength, frequency, and the speed at which a wave travels through its medium (propagation speed, v) are related by:

v = fλ

This equation applies to every wave type the MCAT covers, mechanical (sound, water, string) and electromagnetic (light) alike, though the value of v depends entirely on the medium and, for light, on whether that medium is a vacuum or a material with a given refractive index. Because v = fλ, frequency and wavelength are inversely proportional for a wave traveling at a fixed speed: raising the frequency shrinks the wavelength proportionally, and vice versa. A wave's frequency is a property of its source and does not change as the wave passes from one medium to another, but its speed — and therefore its wavelength — does change with the medium. This exact relationship becomes central later in the guide, first when comparing how sound propagates through air, soft tissue, and bone, and again when analyzing how light refracts at the boundary between two optical media.

Worked Example: Frequency, Wavelength, and Speed

A tuning fork vibrates at a frequency of 440 Hz — concert-pitch A, a note frequently used in illustrative MCAT passages — and produces a sound wave that travels through air at 340 m/s (a no-calculator-friendly approximation to 343 m/s).

Step 1 — Find the period.

T = 1/f = 1/440 Hz ≈ 0.0023 s (about 2.3 ms)

Step 2 — Find the wavelength in air.

Rearranging v = fλ: λ = v/f = (340 m/s)/(440 Hz) ≈ 0.77 m

Step 3 — Predict what happens if the same sound wave enters water (v ≈ 1,480 m/s ≈ 1,500 m/s for estimation).

The tuning fork's frequency is fixed by its source, so 440 Hz does not change when the wave enters a new medium:

λ_water ≈ (1,500 m/s)/(440 Hz) ≈ 3.4 m

The wavelength roughly quadruples in water even though frequency stays exactly the same, because propagation speed depends on the medium's density and elastic (stiffness) properties, not on the source. This frequency-invariant, wavelength-shifting pattern reappears later in the guide when analyzing refraction of light at the boundary between two optical media, and when comparing how sound propagates through air, soft tissue, and bone during auscultation and diagnostic ultrasound — the same v = fλ bookkeeping, just with different propagation speeds for each tissue type.

Simple harmonic motion energy note: For a mass-spring oscillator, total mechanical energy is ½kA² (constant if undamped). At maximum displacement, energy is all elastic PE; at equilibrium, energy is all KE. That energy partition is the oscillatory version of the conservation ideas from the previous section and links periodic motion back to Content Category 4A as a whole.