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DSP for Artists

Sound can be described as a signal that changes over time. A sine wave is a useful place to begin: a smooth, repeating oscillation with just one frequency.

Frequency and amplitude

Frequency is the number of cycles per second, measured in hertz (Hz). Amplitude describes the size of the oscillation. In this example, the vertical axis is normalized from −1 to 1, and the horizontal axis shows one second.

Move the sliders to see how these two properties change the wave.

Wave explorer

One second of a sine wave

10−10 s1 s

Frequency: 3 Hz

Amplitude: 0.65

Try it

  1. Increase the frequency. More cycles fit into the same one-second window.
  2. Reduce the amplitude. The wave gets shorter without changing its frequency.
  3. Set the amplitude to zero. The oscillation becomes a flat line.

The curve follows this expression, where t is time in seconds:

amplitude * Math.sin(2 * Math.PI * frequency * t)

This is a visual example: the frequencies are deliberately slow enough to count, and the explorer does not generate audio.