Fourier Synthesizer

Equipment:

  • Fourier Synthesizer
  • Speaker
  • Oscilloscope
  • proper cables needed

Demo:

This apparatus consists of five independent generators of sine waves. Amplitudes and phases can be varied to create square, triangle, saw-tooth waves and all sorts of wave patterns. Use the combined output to see and listen to the superposition of the waves. Use the mon output to listen to certain channels. If you would like to use an online version of a fourier synthesizer go to this website to add up to 8 sine waves. https://soundphysics.ius.edu/?page_id=949

Explanation:

A pure tone is a sine wave at a specific frequency. If several pure tones are heard simultaneously, the pressure of the sound wave traveling through air wouldn’t be a single sine wave. These tones put together is the sum of the sine functions. The fundamental frequency is joined by different harmonics of frequencies, times the frequency of the fundamental. The combination of the fundamental gives a periodic function with the period of the fundamental.The combination of the fundamental gives a periodic function with the period of the fundamental.Given the function, one can find the sum of the terms with respect to the harmonics. Most of the time all of the harmonics will be required and result in an infinite series called the Fourier series. The process of breaking down the harmonics is called harmonic analysis.

This demonstration shows the sum of up to 5 harmonics of a sine wave.

Notes:

  • If you have the amplitude too high you can cause the wave to not be sinusoidal, but square because it cannot use enough energy to create the entire waveform.

Written by Nick McCabe