Fourier Synthesis

Purpose

To demonstrate Fourier synthesis of complex wave shapes.

Equipment

Fourier synthesizer, dual trace oscilloscope, and loudspeaker on scope/TV cart, as photographed.

Suggestions

Practice for most effective use.

Setup Time

5 min.

Images

h4-01

Description

: Complex waves may be formed using up to twelve harmonics with independently variable amplitudes and phases. Any individual harmonic such as the fundamental (in the photograph above) can be shown on one trace of the oscilloscope, while the sum is shown on the other trace. The wave can be simultaneously seen on the oscilloscope and heard using a loudspeaker with a separate volume control. Digital phase locking of all harmonics allows the frequency to be varied from below 100 Hz to above 1000 Hz while the wave shapes remain fixed, to show that timbre is primarily dependent on harmonic structure

References

T. A. Clark, Versatile Electromechanical Fourier Synthesizer for Laboratory or Lecture Demonstration, AJP 40, 937-942, (1972). Joseph E. Kasper and Alfred F. Benedek, A Versatile Wave Phenomena Device for Use in Demonstrations and in the Laboratory, AJP 42, 754-759 (1974). ◙Geoffrey Whaite and Joe Wolfe, Harmonic or Fourier Synthesis in the Teaching Laboratory, AJP 58, 481-483, (1990). Ayra, Elem. Mod. Physics, Wave-Packet Description of Material Particles, 93.