PURPOSE: To illustrate Ohm's Law of Hearing, and to hear the sounds of complex waves produced by the Fourier Synthesizer.
DESCRIPTION: A Fourier Synthesizer including 12 harmonics with independently adjustable amplitudes and phases is connected to an oscilloscope and loudspeaker. Several relevant demonstrations can be performed using this setup: (1) Produce various wave shapes. Listen to the difference in sound as each harmonic is added while the wave is being synthesized. Compare the sounds of the different wave shapes. (2) Demonstrate that although the wave shape changes when the phase of any of the harmonics is changed, change of phase of harmonics has a negligible effect on the timbre or tone quality. Ohm's Law of Hearing states that the sound of a complex tone is to a great degree independent of the phases of the harmonics. (3) Remove the fundamental from a complex tone - best for the pulse train, which has large-amplitude harmonics. The frequency of the fundamental is still audible due to difference tones created by the non-linear mechanism of the ear. The frequency of a complex wave is due in large part to the combined effect of all of the harmonics, illustrating the "missing fundamental."(4) Demonstrate fundamental tracking by varying the frequency of the synthesizer with the fundamental missing. The ear follows the missing fundamental frequency.
REFERENCES: (PIRA unavailable.) See Demonstration Reference File for information about the synthesizer and about Ohm's Law of Hearing.
EQUIPMENT: Fourier Synthesizer with loudspeaker and dual trace oscilloscope on scope/TV cart.
SETUP TIME: 5 min.
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