The vibration of the diaphragm and the human eardrum is a fascinating topic within the realm of auditory perception. Understanding how these structures respond to sound waves is crucial for grasping the intricacies of how we hear multiple pitches at once. This article delves into the mechanics behind the eardrum's vibration when exposed to sounds with multiple frequencies, highlighting the difference between individual frequency vibration and the summation of all frequencies present.

Introduction to Diaphragm and Eardrum Vibration

The eardrum, a thin, flexible membrane, vibrates in response to sound waves. When hit with a voice containing multiple frequencies, the eardrum does not vibrate solely at the average frequency. Instead, it vibrates at the sum of all individual frequencies. This phenomenon can be likened to the way water height at a specific point moves up and down due to a combination of large and small waves all acting together.

Vibration Mechanism of the Eardrum

The interior of the eardrum, or tympanum, behaves more like an exponentially variable thickness hollow channel. Each thickness section resonates at a different frequency, ranging from 10 Hz to 20 kHz. This complex interaction means that the eardrum vibrates at all the incoming frequencies simultaneously, rather than a single average frequency. This ability to handle multiple frequencies concurrently is what allows us to hear more than one pitch at a time.

Summation and Bandwidth Filtering

When sound waves of different frequencies hit the eardrum, the vibration is the summation of cosines, rather than a simple averaging of frequencies. However, the human ear has a limited bandwidth, and high-frequency components are filtered out, which is why we cannot perceive all frequencies equally.

The Basilar Membrane's Role

The basilar membrane, a part of the cochlea, further complicates and enriches this process. The basilar membrane is a long, rolled-up structure that vibrates at specific locations depending on the frequency of the sound. When multiple tones are present, each tone causes the membrane to vibrate at its corresponding location. This spatial mapping allows for the differentiation of various frequencies, contributing to the rich and complex nature of sound perception.

Subjective vs. Objective Perception

The brain's analysis of sound can differ from the objective frequency response. While the cochlea processes frequencies, the brain may favor time-based analysis of waveforms. This discrepancy explains why adding a super-tweeter to a speaker system can enhance the subjective quality of sound, even though the higher frequencies are inaudible as steady tones.

Conclusion

Understanding the vibration of the diaphragm and human eardrum is essential for comprehending auditory perception. The eardrum's ability to vibrate at the sum of all incoming frequencies, rather than a single average frequency, is a remarkable feat of biological engineering. This complex vibration process, facilitated by the basilar membrane and the brain's analysis, allows us to perceive and appreciate the rich and diverse world of sound.

Keywords: diaphragm vibration, human eardrum, frequency summation