Sine Wave Lab
Explore amplitude, frequency and phase in an animated sine wave.
Explore the lab
What you can explore
- Amplitude
Change A to raise or lower peaks while keeping the cycle spacing unchanged.
- Frequency and motion
Change B to alter both spatial cycle spacing and the time-dependent oscillation in this linked model.
- Phase and key points
Adjust phase in degrees and display key points to locate shifted zeros, peaks and troughs.
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The model
Formula and underlying model
y(x,t) = A sin(Bx + φ − Bt)- A
- Amplitude (graph units)
- B
- Linked spatial and temporal frequency parameter (abstract units)
- φ
- Phase offset; entered in degrees and converted internally (radians in formula)
- x, t
- Graph position and elapsed animation time (graph units; s)
This Math model uses the same B in Bx and Bt. Spatial and temporal frequencies are linked, not independently editable k and ω.
The experiment
How it works
Set the wave
Choose amplitude, B and phase to define the curve.
Advance time
Play or scrub the timeline to change the −Bt term.
Inspect cycles
Compare peak height, zeros and cycle spacing using the graph markers.
Learning outcomes
What you’ll learn
- Distinguish amplitude changes from phase shifts.
- Explain how B links spatial spacing and temporal oscillation.
- Locate peaks and zeros on a sine curve.
Keep exploring
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Ready to experiment?
Explore Sine Wave interactively
Open the lab, adjust the parameters, and see the results change in real time.