40. Fourier Analysis and Synthesis

The Pasco Fourier synthesizer produces two 440 Hz fundamentals and eight exact harmonics. You can vary the amplitude and phase of any of these signals and add them up to generate a complex wave form. The output goes to an oscilloscope and also to a speaker so the class can hear the wave form. The two fundamentals can be added alone to show the sum of two sine waves, or sent to two speakers to demonstrate acoustical interference.

The Fourier analyzer shows the power spectrum of a complex wave form on an oscilloscope.

Applet by Fu-Kwun Hwang --- Virtual Physics Library

How to play:

  1. Left click and drag the [blue or green ball] circles to change the magnitude of each Fourier functions [Sin nf, Cos nf].
  2. Right click the mouse button to change the magnitude between 0 and 1.0
  3. Click Play to turn on the sound effect, Stop to turn it off.
  4. The coefficient of sin(0f) is used as an amplification factor for all modes (Use it to change the sound level). The coefficient of cos(0f) is the DC component.
  5. Click the checkbox at the top (after hitting Stop) to show the square of the amplitude of the signal.

The default value for base frequency is f=100Hz, you can change it from the TextField (20 < f < 2000). The ear is 1000 times more sensitive at 1kHz than at 100Hz.

  frequency range
speech song
adult male 80-240 up to 700
adult female 140-500 up to 1100