Mason Blake
The concept of zero in relation to sound is complex and multifaceted. In mathematics, zero typically signifies a null quantity, suggesting that 0 decibels (dB) should equate to silence or the absence of sound. However, this notion is misleading, as 0 dB does not represent total silence in the context of sound measurement. In audio recording, 0 dB is often associated with the loudest level before distortion occurs, contrary to the idea of silence. This discrepancy arises from the use of dBFS (decibels relative to Full Scale), where 0 dBFS corresponds to the maximum signal level. Exploring the concept further, we encounter the notion of zero sound in quantum mechanics, described as unique quantum vibrations in quantum Fermi liquids. Additionally, in the field of audio engineering, the threshold of human hearing is considered to be around 0 dB, with values below this threshold perceived as very faint sounds. Achieving a true 0 dB reading in a quiet room is challenging due to various factors, including bodily functions and ambient noise.
| Characteristics | Values |
|---|---|
| Zero sound | Unique quantum vibrations in quantum Fermi liquids |
| Zero sound propagation | Direction of the head of the Fermi surface with no change in liquid density |
| Zero sound waves | Fluctuations in space and time of the quasiparticles' momentum distribution function |
| Zero hertz | Zero cycles per second, no sound |
| 0 dB | Lowest sound perceived by the human ear, not total silence |
| dBFS | Decibels relative to Full Scale |
| dBFS 0 | Maximum signal level possible |
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What You'll Learn
Zero sound and quantum vibrations
In the context of sound, "zero" typically refers to the absence of sound, representing total silence. This is often associated with 0 decibels (dB), which corresponds to the absence of sound or the lowest point in terms of volume. However, it is important to note that in audio recording, 0 dB is the loudest level possible.
Now, delving into the concept of "Zero Sound," it is a term coined by Lev Landau in 1957 to describe the unique quantum vibrations in quantum Fermi liquids. Zero sound goes beyond the simple wave of compression and rarefaction and is instead a fluctuation in space and time of the quasiparticles' momentum distribution function. As the Fermi distribution function changes, zero sound propagates in the direction of the Fermi surface without altering the liquid's density. This phenomenon played a pivotal role in confirming the correctness of Landau's Fermi liquid theory.
The transition from classical to quantum behavior of sound is often observed in the quantum ground state, where the number of phonons, or acoustic phonons, is minimized or close to zero. This reduction in phonons, achieved through cooling techniques, helps eliminate unwanted noise and facilitates the study of single quanta of sound. It also bridges the gap between classical and quantum mechanics, providing deeper insights into the fundamental nature of matter.
Furthermore, the concept of zero sound relates to the dispersion relation for zero sound waves and the ratio of zero sound phase velocity to Fermi velocity. This involves the Landau parameter, which influences the behavior of zero sound waves. Understanding zero sound has implications for quantum communication systems and future quantum technologies, as it enables the minimization of thermal noise and the exploration of quantum effects.
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Zero decibels and silence
Decibels are ratios, and they only have meaning when compared to something else. While it may seem intuitive that total silence, or a complete absence of sound, would be equivalent to 0 decibels, this is not the case. In the context of sound as a potential hazard in the workplace, zero can indicate the lowest level of sound, but in audio recording, 0 dB is typically the loudest that the audio can be before causing distortion. This is because the audio is being measured in dBFS, or decibels relative to Full Scale, where 0 dBFS is the maximum signal level possible.
In reality, 0 dB represents the threshold of human hearing, and values close to 0 dB imply the perception of very faint sounds. A reading of 0 dB would only occur in a room where all the sounds are so soft that they cannot be perceived by the human ear. These places are called anechoic chambers, which are set up by scientists researching the intensity of sound. Even in these environments, a person stepping into the room would cause the dB reading to rise above zero.
The human ear can perceive a wide range of sounds, and its built-in mechanism works to moderate sensitivity to sounds as they become higher and louder, allowing it to tolerate a broad range of sound levels. The lowest sound that can typically be heard by humans is 20 Hz, and anything above 80 dB can cause hearing damage over extended periods.
Zero hertz means zero cycles per second, which means nothing is changing and there is no sound. Negative hertz does not make sense because it is not possible to have a negative amount of something per second.
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Zero hertz and silent DC signals
In the context of sound, zero hertz means zero cycles per second, indicating that nothing is changing and there is an absence of sound. This corresponds to a Direct Current (DC) signal, which also has a frequency of zero as there is no repetitive pattern.
In audio recording, decibels (dB) are used to measure loudness, and it would be intuitive to assume that total silence or the absence of sound would be represented as 0 dB. However, this is not always the case. 0 dB can represent the loudest possible signal level, and silence is measured as a negative number. This is because the decibel system is based on ratios and is relative to Full Scale (dBFS).
While it is commonly understood that DC signals have a frequency of zero hertz, some sources argue that this is not a useful way to conceptualize DC. They argue that in reality, there is no such thing as a true DC signal as all signals have some variability. Additionally, when considering the Fourier transform of a DC signal, it can be seen as a circle with its centre of mass always at zero, resulting in all frequencies having zero amplitude.
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Zero sound and Fermi liquids
Zero sound, a term coined by Lev Landau in 1957, refers to the unique quantum vibrations in quantum Fermi liquids. It is a fluctuation in space and time of the quasiparticles' momentum distribution function, rather than a simple wave of compression and rarefaction. As the Fermi distribution function changes, zero sound propagates towards the head of the Fermi surface without altering the liquid's density.
The Boltzmann transport equation for general systems in the semiclassical limit describes the behaviour of zero sound in Fermi liquids. The zero sound waves' dispersion relation is given by the functional operator equation, which involves the collision functional and the energy of a quasiparticle of momentum. The ratio of zero sound phase velocity to Fermi velocity is also defined by the dispersion relation.
The Fermi liquid theory, proposed by Landau, is supported by experimental observations of zero sound. This theory, which includes the Boltzmann transport equation, is applicable to Fermi liquids, where the energy of a quasiparticle is influenced by its momentum and the normalized Landau parameter.
The zero angular momentum longitudinal vibrations of the Fermi surface in Landau's Fermi liquid theory exhibit a linear-in-wavenumber dispersion, corresponding to zero sound. However, when weak Coulomb interactions are introduced, it transforms into a plasmon mode, dispersing as the square root of the wavenumber. Interestingly, despite the fundamental differences between Fermi liquids and non-Fermi liquids (NFL), the zero sound and plasmon modes behave similarly in both systems.
In the context of audio recording, zero typically signifies silence or the absence of sound, represented as 0 dB or 0 dBFS, respectively. In decibels (dB), 0 dB indicates silence, while in dBFS, it represents the maximum signal level, with all other measurements being negative.
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Zero sound and Landau's Fermi liquid theory
In audio recording, 0 dBFS (decibels relative to Full Scale) is the maximum signal level possible, and is hence the loudest that the audio can go before it starts to distort. Thus, 0 dBFS does not refer to the absence of sound. However, 0 decibels can mean the absence of sound in certain contexts, such as when talking about sound as a hazard in the workplace.
Zero sound, a term coined by Lev Landau in 1957, refers to the unique quantum vibrations in quantum Fermi liquids. It can be described as a fluctuation in space and time of the quasiparticles' momentum distribution function. As the shape of the Fermi distribution function changes, zero sound propagates in the direction of the head of the Fermi surface without any change in the density of the liquid.
The Fermi liquid theory describes the energy of a quasiparticle of momentum as a function of the Landau parameter and other variables. Landau predicted that transverse sound propagates in a Fermi liquid with sufficiently strong Fermi liquid interactions, unlike classical fluids that cannot support shear oscillations. Zero sound was thus one of the key confirmations of the correctness of Landau's Fermi liquid theory.
The ratio of zero sound phase velocity to Fermi velocity is given by the equation s = ω/kVF. The dispersion relation for the zero sound waves can be determined using a functional operator equation.
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Frequently asked questions
Zero is often associated with silence, but in audio recording, 0dB is the loudest that the audio can go before it starts to distort.
0dB is the lowest sound perceived by the human ear. It does not mean total silence, as even in a quiet room, a person's breathing would be recorded at 10dB.
Decibels are units of measurement for sound. They are ratios and only mean something when compared to something else.
The threshold of human hearing ranges from 0 to 140dB, with values ranging from less harmful to more harmful to our health.
