Sine Wave Calculator: Amplitude, Frequency, and Phase Explained
The sine wave is the fundamental building block of periodic signals. Every complex periodic signal — sound, light, radio waves, AC electrical current — can be decomposed into a sum of sine waves (Fourier analysis). Understanding the parameters that describe a sine wave is the foundation of signal processing, acoustics, and electronics.
The General Form
y(t) = A × sin(2πft + φ)
Where:
- A = Amplitude (peak value)
- f = Frequency in Hz (cycles per second)
- t = Time
- φ (phi) = Phase shift (horizontal offset in radians)
- 2πf = Angular frequency ω (omega), in radians per second
What Each Parameter Does
Amplitude: how tall the wave is. Doubles the amplitude = doubles the peak value = increases power by 4× (power is proportional to amplitude²). In audio: amplitude corresponds to loudness.
Frequency: how many complete cycles per second. Middle C on a piano: 261.63 Hz. A440 (standard tuning A): 440 Hz. Doubling frequency raises pitch by one octave.
Period: T = 1/f. How long one complete cycle takes. A 440 Hz sine wave has a period of 1/440 ≈ 2.27 milliseconds.
Phase shift: horizontal offset of the wave. Two sine waves with the same frequency but opposite phase (180° apart) cancel each other out — this is how noise-canceling headphones work.
AC Electricity
US household current is a sine wave: 120V RMS (root mean square) at 60 Hz. The actual peak voltage is 120 × √2 ≈ 170V. RMS is the effective voltage for power calculations.
European standard: 230V RMS at 50 Hz.
[Visualize sine waves →](https://doesitaddup.com)
Frequently Asked Questions
Why is my calculated peak voltage different from the voltage rating on my electrical outlet?
Electrical outlets are labeled in RMS (root mean square) voltage, not peak voltage. US household current is 120V RMS, but the actual peak voltage of the sine wave is 120 × √2 ≈ 170V. RMS represents the effective voltage for power calculations, which is why devices are rated in RMS rather than peak values.
How do I calculate the period of a sine wave if I only know the frequency?
Use the formula T = 1/f, where T is the period in seconds and f is the frequency in Hz. For example, a 440 Hz sine wave (A440 musical note) has a period of 1/440 ≈ 2.27 milliseconds, meaning one complete cycle takes about 2.27 ms to finish.
If I double the amplitude of a sine wave, does the power also double?
No—power is proportional to amplitude squared, not amplitude itself. If you double the amplitude, the power increases by 4× (2² = 4). This is why small changes in amplitude can have dramatic effects on signal power in audio and radio applications.
What does phase shift actually mean, and when would I use it?
Phase shift is a horizontal offset of the sine wave, measured in radians or degrees. Two sine waves with identical frequency but 180° opposite phase will completely cancel each other out—this principle is how noise-canceling headphones work by generating an inverted sine wave to eliminate unwanted sound.
This article is for informational purposes only. See our disclaimer.