You will be able to
- Relate frequency to period and amplitude to scale.
- Predict how phase changes the starting point without changing frequency.
Three independent controls
A sinusoid is a regular oscillation. Amplitude A sets its peak size, frequency f counts cycles per second, and phase φ sets where the cycle begins. Sine takes an angle in radians. One complete turn is 2π radians or 360°. Negative amplitude can be rewritten as positive amplitude plus a half-turn of phase.
Add waves, not their descriptions
Two waveforms add sample by sample. Matching frequencies may reinforce or cancel depending on phase; different frequencies form a more complex shape. The frequency-domain view helps separate those components, but phase still matters when reconstructing their sum.
Worked example
A 5 Hz sinusoid has period 0.2 s. At t=0, A=2 and φ=π/2 give x(0)=2. A phase change does not change its 5 cycles/s.
A common trap
A bigger waveform is not necessarily a higher-frequency waveform. Loudness also depends on perception and is not simply peak amplitude.
Predict, then experiment
What happens to the sum of two equal-frequency, equal-amplitude tones separated by 180°? Before touching the controls, say or write your prediction.
Interactive experiment
Harmonic composer
How do amplitude, frequency and phase appear in a discrete spectrum?
The waveform is the sample-wise sum; its vertical scale is automatic and labelled. The spectrum view shows 0–16 Hz of the available 0–32 Hz band. Bars use the left amplitude scale; phase points use the right −π to +π radian scale. Phase is omitted below amplitude 0.03.
Your experiment
Set both frequencies to 4 Hz and both amplitudes to 1. Set phases to 0° and 180°. Compare the cancellation with both phases at 0°; then set one frequency to 4.25 Hz.
Change one parameter at a time. Compare what you observed with your prediction and record an explanation in your notes.
Check your understanding
Try from memory first. Hints and feedback are part of learning, not a penalty. These checks are for self-study, not a graded qualification.
Reference answers (after your attempt)
- Frequency — Correct: T=1/f.
- 0.125s — T=1/8 = 0.125 s.
Apply it: Predict before plotting
Use paper, your notes, or a local notebook/editor. Code examples are Python 3 starting points to run yourself; this page does not execute code or automatically assess the practical task.
- Write the value at t=0 for A=3, f=2 Hz, φ=0.
- Repeat for φ=π/2.
- Explain why both have the same period.
Reference solution & review criteria
The initial values are 0 and 3; both periods are 0.5 s because phase changes neither f nor T.
Your notebook
Notes and progress stay in this browser. They are not sent to the server; ordinary web-server request logs still operate. Export a backup from the course page.
Completion requires both correct checks and your practical-task acknowledgement.
Go deeper
Sources support further study; the worked examples and questions here are original. Browser experiments are small, disclosed models—not evidence of production-model quality or hardware performance.