Periodic Waves
A periodic wave repeats in time and space. Period and frequency are reciprocals, wavelength is the spatial repeat distance, and wave speed connects frequency and wavelength through v=fλ; at a fixed point or fixed instant, sinusoidal graphs reveal amplitude, period, wavelength, and phase.
Periodic Waves: quick answer
A periodic wave repeats in time and space. Period and frequency are reciprocals, wavelength is the spatial repeat distance, and wave speed connects frequency and wavelength through v=fλ; at a fixed point or fixed instant, sinusoidal graphs reveal amplitude, period, wavelength, and phase. Periodic-wave problems become simple when you separate what repeats in time from what repeats in space. A time graph gives T; a position snapshot gives λ; the medium speed then links them through v=fλ.
Do not infer amplitude from frequency: amplitude is independent of period and frequency. When a source frequency changes in an unchanged medium, use the medium speed to reason about the corresponding wavelength.
What you should be able to explain and do
Use these as closed-note retrieval prompts before opening the worked reasoning.
Read period and amplitude from displacement-versus-time graphs.
Read wavelength and amplitude from displacement-versus-position snapshots.
Use T=1/f and v=fλ with consistent units.
Explain how wavelength changes when source frequency changes while medium speed stays fixed.
Key terms for this wave model
Definitions stay next to the model so no important term requires leaving the lesson to understand the explanation.
period
period is the time for one complete cycle, measured in seconds.
frequency
frequency is the number of cycles per second, measured in hertz.
wavelength
wavelength is the shortest spatial separation between points in the same phase, measured in meters.
amplitude
amplitude is the maximum displacement or disturbance magnitude from equilibrium.
phase
phase is where a point lies within a repeating wave cycle.
crest and trough
crest and trough is maximum positive and negative displacement locations in a transverse sinusoidal representation.
Match every relationship to its conditions
Some Unit 14 relationships are intentionally qualitative. Keep the variable meanings, geometry, and scope attached to each statement.
| Relationship / model | Variables & units / meaning | When to use it | Physical anchor |
|---|---|---|---|
v = fλ | v wave speed (m/s); f frequency (Hz); λ wavelength (m) | any periodic wave when speed, frequency, and wavelength refer to the same wave in the same medium | at v=12 m/s and f=4 Hz, λ=3 m |
T = 1/f | T period (s); f frequency (Hz) | converting between temporal repeat time and cycles per second | a 50 Hz wave has T=0.020 s |
sinusoidal wave: y(x)=A sin(2πx/λ+φ) | y displacement (m); A amplitude (m); x position (m); λ wavelength (m); φ phase constant (rad) | reading or constructing a sinusoidal displacement-versus-position representation at a fixed instant | successive crests are separated by one wavelength |
What the diagram or graph must show
Translate physical situation ↔ diagram/graph ↔ relationship ↔ verbal prediction.
Time graph
horizontal spacing between matching phases is T.
Position graph
horizontal spacing between matching phases is λ.
Phase map
points separated by one wavelength are in the same phase.
Trend map
fixed medium speed means f↑ produces λ↓.
Change one wave condition and inspect what responds
Predict first, then move one control. The tool is constrained to the topic model rather than introducing extra equations.
Two examples with model selection exposed
Each example identifies the representation/condition before the arithmetic or qualitative conclusion.
Frequency and wavelength
Situation: A wave travels at 18 m/s and has period 0.25 s.
Reasoning: f=1/T=4.0 Hz; then λ=v/f.
λ=4.5 m.
Changed source frequency
Situation: A source doubles its frequency while the medium is unchanged.
Reasoning: The wave speed remains set by the medium; v=fλ means λ must halve.
Frequency ×2, wavelength ×1/2, speed unchanged.
Recognize the physics before reaching for an equation
Use the cue to choose the model, connect it to nearby ideas, then reject any method whose assumptions do not match the situation.
What should trigger Topic 14.2?
Use periodic-wave relationships when frequency, period, wavelength, wave speed, or phase repeats regularly in space and time.
How this idea fits the course
The wavelength/frequency framework becomes the quantitative backbone for standing waves, diffraction, and optical interference.
Scope check before solving
Do not infer amplitude from frequency: amplitude is independent of period and frequency. When a source frequency changes in an unchanged medium, use the medium speed to reason about the corresponding wavelength.
Turn the model into measurable evidence
Plan what changes, what is measured, which representation tests the model, and what uncertainty would weaken the conclusion.
Investigation target
Generate periodic waves at several frequencies in the same medium, measure wavelength, and test whether the product fλ remains consistent with the measured propagation speed.
Reasoning errors to eliminate
Repair the representation or scope decision before doing more arithmetic.
Six things to do before moving on
Use these as closed-note transfer prompts.
- I can identify the relevant wave representation before choosing an equation.
- I can define every wavelength, frequency, period, angle, aperture/slit spacing, index, or film thickness I use.
- I can predict the qualitative trend before calculating a numerical result.
- I can state when a relationship is qualitative-only or relies on a small-angle/normal-incidence assumption.
- I can translate between physical pattern, diagram/graph, equation/model statement, and verbal claim.
- I can design or critique a wave experiment and justify a conclusion from data and uncertainty.
Practice is kept on its dedicated pages
Finish the lesson first. Then open the separate topic bank when you want exam-style practice without replacing the teaching content above.
42 multiple-choice questions
Use the exact-topic MCQ bank to test model selection, representations, calculations and boundaries after learning the concept.
Open 42 Topic MCQs4 multipart free-response tasks
Use the exact-topic FRQ set for mathematical, representation, experimental and qualitative/quantitative reasoning.
Open 4 Topic FRQsTopic 14.2 FAQs
What is the difference between T and λ?
T is a time interval; λ is a spatial repeat distance.
What is measured in hertz?
Frequency, cycles per second.
If f increases at fixed wave speed, what happens to λ?
It decreases inversely.
Does larger amplitude mean higher frequency?
No. They describe different wave properties.
How do I recognize same phase?
Points one whole wavelength apart in a spatial snapshot have the same phase.