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Writer's pictureHui Wang

103. The Representation of Sound (1)

Updated: Jan 19


'Sound,' a physical phenomenon so familiar to us in our daily lives. From singing to the melodies in our ears, to the conversations stored on our phones, especially for those in audio and video development, dealing with vast amounts of sound data. But do you truly understand the essence of 'sound'?


If you're confident and think 'of course,' consider this: What happens in the transition from 'sound' as we hear it, to the 'audio data' we process with our phones and computers? If this question makes you ponder, join us in a deeper exploration: How does audio data in daily development transform from a mere physical phenomenon into the digital signals in our hands? This exploration may seem trivial, but it can be unexpectedly interesting.


This inquiry involves at least two major cognitive processes: Firstly, using scientific methods to define, explore, discover, and mathematically describe this everyday physical phenomenon. Secondly, the process of digitizing this physical phenomenon.


Looking at this issue from another perspective, we might break it down into several sub-questions:


  • What is the definition of sound? We need to define the scope of this physical phenomenon to study it further.

  • What are the characteristics of sound? Exploring these characteristics helps us describe and study sound more accurately.

  • How do we mathematically describe sound? Mathematics, as the best language for exploring physical laws, is also the foundation for digitizing these phenomena.

  • How do we digitize sound? Digitization is the bridge from the physical to the information world.

  • What is digital audio data? Once sound is processed digitally, it becomes digital audio data that can be processed, stored, or transmitted.


What exactly is sound, this friend that accompanies us day and night?


In the world of science, 'sound' is defined as a magical kind of wave. It's created by vibrations that travel through air, water, and even solid walls, eventually reaching our ears and awakening our sense of hearing. This definition places sound within the category of 'waves' in physics, allowing us to examine and interpret it scientifically. However, just as countless revolutions in knowledge have happened in history, today's definition might be overturned by new discoveries tomorrow. Who can really say for sure?


What magical powers does sound, this invisible artist, possess?


To unveil its mysteries, we first need to listen with our ears. The human auditory system is like a complex and delicate palace, as shown in the diagram. Sound, a traveler through the air, comes as a mechanical wave, crossing vast spaces to knock on the doors of our ears. In this marvelous process, it transforms into the language of nerves, traveling through neural corridors to finally reach our brain, awakening our perception. The finer secrets behind this are like pearls hidden in the deep sea, waiting for brave explorers to discover them.



The characteristics of sound are like pearls we gradually collect from the vast ocean of auditory experiences. As we continuously listen and explore the fascinating world of sound, these features begin to reveal their unique brilliance. Some sounds are as loud as thunder, others as soft as silk; some are sharp and piercing, others deep and warm. We can even recognize individuals from their voices, even if they are of similar loudness. Summarizing these perceptions, we distill the features of sound.


Now we understand these features as the well-known 'three elements of sound': loudness, pitch, and timbre.

  • Loudness describes the strength of sound, pitch its highness or lowness, and timbre its unique quality.

Guided by these features, we delve deeper, uncovering the deeper laws and cause-effect relationships of sound, vividly presenting them in various forms.


For example, the sounds we often hear are the result of object vibrations causing air molecules to arrange in a specific frequency, creating the journey of sound propagation.



When we choose a tiny point to explore how its air pressure changes over time, we are essentially embarking on a journey through time and space. We use a horizontal axis to represent the passage of time and a vertical axis to depict the fluctuations of air pressure, thus creating a waveform chart. This chart is like a still dancer, silently narrating the story of the changing air pressure.



In the world woven by air pressure and sound, the greater the deviation of air pressure from its standard value, the more intense the vibration, much like the fervor of a dance. A waveform with a larger amplitude is like a dancer's more passionate leap, indicating a stronger sound, or greater loudness. Similarly, the closeness of the waveform resembles the rhythm of the dance, where a denser waveform means more steps in a unit of time, a higher frequency, and thus a higher pitch.


Observing a waveform of a single-frequency vibration is like appreciating a simple and clear dance. However, in real life, the sounds we hear are often a mix of multiple complex vibrations, as shown in the following chart. It's like watching many dancers weaving together a complex and fascinating dance on the same stage.




In this complex dance of the waveform chart, the useful information of sound seems hidden, as the waves of various frequencies interweave, much like a complex symphony. In such situations, we turn to the spectrum chart for guidance.


So, how does a spectrum chart come to be? Let’s explore the following chart, which acts like a detailed map revealing the secrets of sound.



A waveform is like a colorful tapestry woven from simple sine waves of multiple frequencies, amplitudes, and phases. The horizontal axis of the waveform chart represents the timeline, while the vertical axis is the stage of amplitude, showing the dance of combined sine wave amplitudes changing over time.


When we apply the magic of Fourier transformation to this composite waveform, it's like stretching a two-dimensional waveform chart into a three-dimensional space, forming a solid model. In this model, the new axis of frequency measures each frequency point, each with its own sine wave dancer moving in unique amplitude and phase.


The spectrum chart is like slicing through this three-dimensional model along the time axis, creating a graph with frequency on the horizontal axis and amplitude on the vertical axis. It captures the distribution of sine wave amplitudes at a static moment across various frequencies.


The waveform chart helps us examine the overall loudness of music, like a telescope for inspecting dynamics and loudness in mixing, aiding in adjusting compressors and limiters. On the other hand, the spectrum chart is like a fine comb, helping us to sort out the distribution of musical details across frequency bands, assisting in fine-tuning with filters and equalizers in mixing.


The following image shows an example of a sound's waveform chart (upper part) and spectrum chart (lower part):



The waveform chart is like a simple narrative poem. Its horizontal axis represents time, and its vertical axis represents loudness, cleverly distinguishing between the left and right audio channels.


On the other hand, the spectrum chart is more like a complex epic. It unfolds in a three-dimensional universe, where time still stretches along the horizontal axis, but the vertical axis is elevated to represent frequency (expressed in musical notes, like A5(880) for 880 Hz), and the brightness of color narrates the changes in loudness. Compared to the waveform chart, the spectrum chart is like a treasure chest filled with more information. Its only shortcoming is that it can't show the overall volume level, so it's often used in conjunction with the waveform chart to reveal the unique characteristics of sound.


 

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