How this instrument works
Many real oscillations — sound waves, alternating electrical current, a swinging pendulum's own displacement — follow the same underlying shape: a plain sine curve, scaled up or down by an amplitude that sets how far the wave swings above and below its center. At any given phase angle θ, the wave's instantaneous value is simply its amplitude A multiplied by sin(θ).
The amplitude changes how TALL the wave's swings are without changing its SHAPE at all — sine's own back-and-forth rhythm (rising to a peak, falling through center, dropping to a trough, and rising again) stays identical regardless of the amplitude; only the scale of that motion changes.
This page accepts the phase angle θ in degrees, radians, or full turns interchangeably — the underlying wave doesn't care which unit describes how far along its own cycle the angle has progressed.
- Enter the wave's amplitude (its maximum swing) into the Amplitude field.
- Enter the phase angle into the θ field.
- Read y: the wave's instantaneous height at that phase angle.
- Try θ=90° to see the wave reach its full amplitude, and θ=0° to see it sit at its center.
Worked example — amplitude 5, θ=30°
A wave with amplitude 5 reaches a height of 5×sin(30°)=2.5 at a phase angle of 30° — the amplitude scales the plain sine curve up or down without changing its overall back-and-forth shape.
At a phase angle of 90°, that same wave reaches its full amplitude, 5 — sine's own peak value of 1, scaled up by the amplitude. At a phase angle of 0°, any wave sits at exactly 0, its center point, regardless of amplitude — sine itself starts at 0.
Questions
What does amplitude control in a wave?
How far the wave swings above and below its own center — a larger amplitude means taller peaks and deeper troughs, while the overall rhythm and shape of the oscillation stays exactly the same.
What does the phase angle represent?
How far along the wave's own repeating cycle a given instant sits — 0° is the wave's center moving upward, 90° is its peak, 180° is center moving downward, and 270° is its trough, with the cycle then repeating.
What real-world phenomena follow this A·sin(θ) shape?
Sound waves, alternating electrical current, a swinging pendulum's displacement, and countless other oscillations — the same amplitude-times-sine relationship describes an enormous range of periodic physical behavior.
What is the wave's value at its peak phase angle?
Exactly its full amplitude — sine itself reaches its maximum value of 1 at a 90° phase angle, so the wave's height there equals A×1=A.
Can the amplitude be zero?
Yes — a wave with zero amplitude has no oscillation at all, sitting flat at 0 regardless of the phase angle, since anything multiplied by zero remains zero.