[ Demos ] [ EECS 20 Home ] [ Corresponding lecture ]

Sums of Sinusoids

This demonstration shows two sinusoids of different frequencies and their sum. The red sinusoid is the sum of the black and blue sinusoids:

[signal display]

The frequencies of the black and blue sinusoids and the phase of the black sinusoid are controlled by a slider in the control panel:

[control panel]

In this illustration, the frequency of the black sinusoid is set to 440 Hz, which is the frequency of the musical note A above middle C. The blue sinusoid is one octave down, at 220 Hz, and hence is also an A.

Observations

Changing the phase of the black sinusoid distinctly changes the shape of the sum (the red sinusoid). However, it does not change the sound. The human ear primarly hears the frequencies of the sinusoidal components of a waveform. It does not hear their phase (at least, not very well). Thus, it is not the shape of a periodic waveform that we hear, but rather the frequencies of its sinusoidal components.