In this blog post, we will examine the scientific principles of hearing through the theories of Fourier, Ohm, and Helmholtz.

The journey to uncovering the secrets of sound: Fourier, Ohm, and Helmholtz

What exactly is the “sound” we hear? If there is a world beyond simple auditory experience, how can we explain the structure of sound and the mechanism of hearing? Scientists have been trying to answer this question for hundreds of years. In this article, we will follow the historical journey of the science of sound in 19th-century Europe, starting with Fourier’s mathematical insights, through Ohm’s theory of hearing, and ending with Helmholtz’s theory of auditory resonance.

Fourier’s theorem: dissecting periodic motion

In 1822, French mathematician Joseph Fourier announced an astonishing mathematical theory.
He claimed that all periodic motion can be expressed as a combination of monochromatic motions with appropriate amplitudes and phases, i.e., sine waves. This theory is now known as “Fourier’s Theorem” and has become a fundamental concept in various fields such as acoustics, thermodynamics, electronics, and signal processing.
Fourier’s theorem is not just a simple mathematical formula, but a key to finding the basic vibration components hidden in complex waveforms. Through this theorem, we have become able to interpret not only sound, but also electromagnetic waves, seismic waves, and even human brain waves, which was the beginning of looking at the invisible world through mathematics.

Ohm’s theory of hearing: Decomposition of complex sounds and perception

Fourier’s mathematical insight was extended to the world of hearing and acoustics in 1843 by German physicist Georg Simon Ohm. Although Ohm is famous for his laws of electricity, he also left an important mark on acoustics.
Ohm thought that if sound is also a periodic physical phenomenon, then it should be possible to break it down into simple components according to Fourier’s theorem. He believed that complex sounds could be broken down into simple sound waves with constant frequencies, or single tones. He argued that most of these single tones have integer multiples of the fundamental frequency, and that the combination of these frequency components creates the unique timbre of musical instruments.
Furthermore, Om believed that the human ear can detect each of these single tones. In other words, although we hear complex musical instrument sounds, we have an auditory experience in which the various single tones contained within them can be recognized individually. He called this the “theory of hearing,” presenting a new perspective in which hearing functions like an analytical machine.

Chladni’s counterargument: Sound is perceived as a “whole”

However, Ohm’s theory of hearing immediately provoked reactions and criticism. At the center of this was German physicist Ernst Chladni Seebeck. He agreed with some of Ohm’s claims, namely that sound is composed of multiple single vibrations, but strongly opposed the claim that each of these single tones can be separated and detected by the ear.
Chladni emphasized that “sound is always perceived as a whole.” He argued that when people hear the sound of a musical instrument, they perceive it as a single tone and do not distinguish the individual frequencies contained within it. His criticism was convincing, and Ohm’s theory, after attracting some attention in the scientific community at the time, gradually fell into oblivion.

The emergence of Helmholtz: The theory of hearing revisited through experimentation

However, Ohm’s idea did not disappear. In 1855, German physiologist and physicist Hermann von Helmholtz revived the idea. He refuted Zebeck’s criticism and sought to provide experimental evidence for Ohm’s theory. He believed that “science is based on hypotheses, but only becomes convincing when proven by experiment.”
Helmholtz used a special experimental device called a glass resonator. This spherical glass device had two mouths of different sizes on either side and had a specific resonant frequency. When a single tone of the same frequency was introduced into the resonator, it vibrated, but did not respond to other sounds. By placing the narrow mouth of the resonator against his ear and listening to complex tones, he was able to determine whether they contained specific frequency components. As a result, it was experimentally proven that the sound of musical instruments is not a single tone, but a complex tone composed of multiple tones. This brought Ohm’s claim back into the spotlight of the scientific community.

Sound synthesis: The birth of a tool for implementing theory

Helmholtz took the experiment one step further. He developed a tuning fork synthesizer and demonstrated that it was possible to produce complex tones similar to those of real musical instruments by sounding tuning forks with different frequencies simultaneously.
This device was a tool that put theory into practice and played a major role in audibly proving how combinations of single tones can produce a variety of timbres. The fact that “sound can not only be broken down, but also recombined” greatly inspired not only acoustics, but also the development of electronic music, digital signal processing, and hearing aids.

Theory of auditory resonance: How does the ear “resonate”?

Helmholtz’s interest now turned to the mechanism of human hearing. He entered the field of auditory physiology with the question, “How can the ear detect individual tones that make up complex sounds?”
In particular, based on his experiments with glass resonators, he reasoned that there must be a structure similar to a resonator inside the ear. Through his “resonance experiments using strings,” he observed that certain strings resonate only at specific frequencies, and he believed that this principle of resonance could also apply to the human body.
What caught his attention was Corti’s organ, discovered in 1851 by anatomist Alfonso Corti. Thousands of Corti’s rods, which are found in the cochlea, vary in size and length and are arranged side by side like the strings of a piano.
Helmholtz believed that these rods resonate at different frequencies and transmit sound to the brain by stimulating the connected auditory nerves. This theory was presented in his “Resonance Theory of Hearing” published in 1863. It was one of the first theories to explain the sense of hearing based on physical principles and became the foundation of modern audiology.

The science of interpreting the senses: Helmholtz’s academic legacy

Although Helmholtz’s theory was supplemented over time, his research remains a pioneering example of interdisciplinary research spanning physics, physiology, and psychology. He transcended the boundaries between what can be seen and heard, demonstrating how scientific imagination and experimentation can lead to profound insights.
The concept of resonance and the experimental techniques he introduced have influenced modern hearing aids, artificial cochlear implants, voice analysis programs, and digital audio technology, and have become important cornerstones in the development of psychoacoustics and neurophysiology.

In conclusion: The scientific meaning of hearing

Although “hearing” seems like a simple act, it encompasses hundreds of years of scientific exploration and theory. Fourier discovered order in complex waveforms, Ohm connected it to hearing, and Helmholtz proved it through experiments and expanded it into physiology. Their journey was not only the development of acoustics, but also a deep philosophical exploration to scientifically explain how we perceive and sense the world. Sound is invisible, but human efforts to understand it are always clear. And that journey continues even now.