Something About Sound And How It Propagates In The Context Of Public Warning Systems – Part 1/2

Listen to audio:

Motto: In fact, it is hearing, not vision, that is the most important social sense of human beings. The auditory system is their most important communication organ. 

Visual Versus Auditory Information System 

A visual early warning system has limited capabilities. Let’s mention just two aspects: range and interpretation by human visual perception. You must be looking in the right direction to register a visual signal. The source of this signal may be behind an unexpected obstacle. You could be in a smoke-filled space, and the brightness of a fire may mask a visual warning signal or instruction. The human eye cannot extract a visual cue from the brightness of flames. The intensity of the flames can blind you, making other aspects imperceptible… 

An acoustic signal is interpreted by humans in a far more complex way. For example, the loss of sound while watching a movie is far more disruptive than the loss of the image. An acoustic warning system, e.g., an evacuation siren, performs its function even in total chaos, when you subconsciously follow its instructions. The auditory system can extract the control instructions of an Emergency Alert System even when the background noise (e.g., collapsing walls, fire roar, etc.) is at the same level as the warning signal, because speech is a correlated signal: individual words logically follow each other. Acoustic instructions are accessible from any position, even in a smoke-filled environment. There is an extensive field of science, psychoacoustics, addressing these and many other aspects. There is no known equivalent in the context of visual perception. 

Information Transmission Through A Medium  

Every transmission of information is conditional upon the transfer of energy. The transport of information, or energy, may or may not require a mediating medium. In the case of sound, the necessary medium is the Earth’s atmosphere. Its advantage is ubiquity, which makes sound a dominant tool for conveying warning information and related instructions via acoustic mass warning systems. 

Earth’s Atmosphere As A Gas  

The enormous mass of air exerts a force on us that we do not even notice. This force, normalized per unit area, defines atmospheric pressure. Atmospheric pressure decreases with altitude and is directly proportional to the density of air molecules (dominated by oxygen and nitrogen). At sea level, atmospheric pressure exerts about 10 tons per square meter. Atmospheric pressure acts equally from all sides, regardless of body position. 

Intermolecular forces in a gas are attractive at very short distances (weak Van der Waals forces) and repulsive at long distances. The repulsive force allows a gas to occupy an unbounded volume. Without gravity, Earth’s atmosphere would disperse; even solar wind would not be necessary. The attractive force draws molecules closer, giving real gas a tendency to occupy a smaller volume than an ideal gas. When, due to a propagating disturbance, oxygen and nitrogen atoms approach each other closely, physical contact occurs because no repulsive force prevents it. Which interaction dominates depends on temperature and pressure. At Earth’s atmospheric pressure and temperature, air remains a gas, and therefore is available for acoustic warning systems. 

What Is Sound 

In the context of sound, atmospheric pressure can be considered constant. The ear does not perceive atmospheric pressure or its slow changes (e.g., due to weather). It is even adapted to such slow changes (Eustachian tube). But: the ear detects very rapid changes in atmospheric pressure. In short, sound is a sufficiently fast (but not too fast) and simultaneously sufficiently large change in current atmospheric pressure. The ear registers pressure changes lasting between 0.050 and 0.000050 seconds. If changes in atmospheric pressure last longer than 0.050 seconds or shorter than 0.000050 seconds, we do not hear them. Once again: the ear detects only rapid dynamics of atmospheric pressure. And it is precisely these rapid changes that warning devices in public warning systems generate. Compared to atmospheric pressure, the amplitudes of these dynamic changes (creating sound) are very small. Expressed as a percentage of atmospheric pressure, they range from 0.000000020% (threshold of hearing) to 0.1% (threshold of discomfort). For illustration: the threshold of hearing corresponds to the buzz of a mosquito three meters away. 

Interpretation Of Sound Generation At The Molecular Level  

Sound particles have minimal, negligible mutual forces. Individual molecules move freely, chaotically, in so-called Brownian motion. This movement also creates rapid dynamic changes in atmospheric pressure, but negligibly small for sound. To generate sound, we must induce rapid collective compression and subsequent rarefaction of particle density, i.e., local atmospheric pressure, which is exactly what an electronic warning device does. Imagine generating this process once. Locally, we create an event—a disturbance in stable atmospheric pressure. We have generated a sound disturbance. Fine—but how does the ear detect it even at a distance? Because this atmospheric disturbance (sound) propagates through space, via the medium, the atmosphere. 

Mechanism Of Acoustic Disturbance Propagation Through The Atmosphere

Note: The verbal description below is visually illustrated in Part 2, so don’t be discouraged. 

Air is compressible (not surprising, as the space between sparsely distributed air molecules is almost a vacuum). 

Let the initial stimulus be, for example, the vibration of a warning device membrane. The membrane collides with the nearest air molecule, molecule #1, imparting momentum and kinetic energy. This first, attacking particle travels a certain distance (dependent on its mass and membrane displacement) and collides with the neighboring particle, molecule #2. This collision is elastic because air molecules are elastic. Only at the moment of impact do intermolecular forces matter. 

The first particle transfers part of its momentum to the second particle according to the law of conservation of momentum, pushing it in the direction of the kinetic force of particle #1. 

The remaining energy excites both particles, possibly imparting rotation. Due to particle elasticity and Newton’s third law, particle #1 is pushed backward—unless it is immediately hit by the next attacking particle #3. Otherwise, particle #1 would simply stop and continue moving chaotically via Brownian motion. 

At each impact and rebound, part of the kinetic energy converts to vibration—resonance of the micro elastic system of the air particle, where the dominant dimensions of the particle periodically change. The molecule is elastic. 

Since the attack occurs at a non-orthogonal angle, the attacked particle gains some rotation. 

These two aspects represent absorption losses in sound propagation. 

The phenomenon occurs collectively and coherently across the entire membrane surface, creating higher molecular density near the membrane and thus increasing pressure. 

During the opposite membrane displacement, the same happens behind the membrane, i.e., in front of the membrane, causing air rarefaction and reduced particle density—negative pressure. 

From the above description, it is clear that particle motion—the ping-pong effect—occurs in the direction of sound propagation. This rapid change in atmospheric pressure travels longitudinally through the air, with particle movement parallel to wave propagation. When a speaker membrane deflects sharply, it triggers a chain reaction allowing efficient propagation of the disturbance as a rapid atmospheric pressure fluctuation. 

Spatial Displacement Of Excited Air Particles

In this context, we speak not of particle vibration but spatial displacement. This aligns with studies determining the maximum displacement of air particles. This displacement depends on the acoustic pressure magnitude. How sharply one particle collides with the next depends on the acoustic pressure vector and the rate of atmospheric change. 

At the hearing threshold, particle displacement is 0.000000000008 meters; for ordinary acoustic pressure, about 0.00000004 meters; at the threshold of discomfort (maximum tolerable pressure), maximum particle displacement is 0.00004 meters. 

For reference: a hydrogen atom is roughly ten times larger than the minimum displacement of an excited air particle. Factually, with minimally audible particle displacement, we may question whether air can still be considered a continuum for sound transmission. 

It is noteworthy that Brownian thermal motion of molecules has an amplitude only an order of magnitude smaller (ten times smaller) than particle displacement at the hearing threshold. The auditory system thus operates at the edge of physical possibility. If it were slightly more sensitive, we could say it could “hear grass grow.” 

The article was written by

Stanislav Gašpar

Stanislav worked in electronics design for a long time before transitioning to acoustics, bringing a nonconformist approach to addressing related topics. Recently, in the context of acoustics, he finds it stimulating to engage with AI, aiming to make it contradict itself and impose his own interpretation of the presented problem. Through years of experience in the technocratic industry, he has come to embrace two guiding principles: reality is orders of magnitude more complex than we interpret it, and the real fun begins when “something doesn’t work.” Additionally, he enjoys expressing his thoughts on poetry and music.

You might be interested