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

Listen to audio:

This article continues from Part 1, which introduced how sound is created and travels through air. In Part 2, we focus on how sound impulses propagate, how particle motion differs from wave motion, and why these principles matter for public warning systems. 

Speed of Sound Particle Motion

To begin, it’s important to clarify one key concept: the speed of air particle movement as a medium for sound transmission is not the same as the speed of sound propagation itself. 

The motion of air particles is proportional to acoustic pressure, but it must not be confused with the speed at which a sound wave travels. 

• At the threshold of hearing, particle velocity is around 0.000000005 m/s 

• Under normal acoustic pressure: 0.00025 m/s 

• At the threshold of discomfort: 0.25 m/s 

Keep in mind that while these particles move extremely slowly, the wavefront of the sound has already traveled roughly 340 meters in the same moment. This clearly shows that the transport of sound energy does not happen through significant movement of the air medium, but through the transmission of energy between particles. 

To illustrate this, let’s use two mechanical analogies that also help to visualize how sound propagates in the first place. 

Creation of a Sound Shock (Impulse) and Its Propagation Speed 

Let us present two examples. While neither perfectly reflects reality—mainly because the particles representing air molecules behave differently in terms of elasticity—they still effectively illustrate how neighboring molecules interact and help clarify the difference between particle speed and the speed of mechanical impulse propagation.

Example 1: Billiard Balls

Let the red ball represent an oxygen molecule (composed of two atoms) with a mass of 5.31×10⁻²⁶ kg. The white ball represents a nitrogen molecule (also composed of two atoms), weighing 4.651×10⁻²⁶ kg. These molecules move chaotically due to Brownian motion; the nitrogen molecule (white ball) spontaneously approaches the oxygen molecule.

Thanks to an external impulse—a billiard cue—the white ball (nitrogen molecule) strikes the red ball (oxygen molecule) forcefully. In this illustrative example, the cue represents the displacement of a speaker diaphragm in a warning device, which similarly impacts surrounding air molecules.

Take note of what happens: the nitrogen molecule, hit by an extremely strong and precisely directed force, remains almost stationary (it only shifts slightly backward in accordance with the law of conservation of momentum). The red oxygen molecule is likewise displaced by the same law and moves away.

Both balls begin to vibrate at their own resonant frequencies, determined by their size, mass, and internal structure—and likely begin to rotate as well. The moment of impact is what we call the impulse. The transfer of momentum or kinetic energy from the white ball to the red ball happens extremely quickly and, in this example, represents the speed of sound propagation.

The red ball itself, however, moves relatively slowly in a forced direction. This represents the actual speed of movement of an air molecule.

The point being made is this:

The speed of sound propagation corresponds to the speed of the impulse, i.e., the speed at which momentum is distributed between molecules.
The particles themselves—during this microscopic ping-pong—move very slowly.

 What is imperfect about this example?

The key shortcoming of this analogy lies in the difference in elasticity between billiard balls and actual air molecules. If the balls possessed the same elasticity as air molecules, the attacking white ball would be equally willing to recoil after impact—assuming an extremely short cue strike. It would bounce back in approximately the opposite direction, depending on the angle and point of contact between the cue and the white ball.

Example 2: Newton’s Cradle

This example is intended to better demonstrate the speed of sound propagation compared to the speed of the particles mediating sound transmission.

Just like the previous example, this one does not fully reflect reality, especially in terms of particle elasticity. In addition, the individual balls of the pendulum are connected by strings fixed to the top of the stand. Each ball therefore forms a mechanical resonant system with its own oscillation period. This period becomes visible when the end ball is displaced into a high position, although in the context of our topic this detail is irrelevant. Only at the initial moment of displacement does the movement of the end ball represent the speed of a particle.

The initial speed of the free swing of this last end ball (E) is proportional to the force with which the impulse was introduced into the row of balls. The entire event begins with the displacement of the opposite end ball (A), whose fall under gravity—possibly reinforced by a manual push—represents the acoustic pressure, or more precisely, the kinetic force distributed across the contact surface between the balls.

In a video recording, you would hardly notice the moment at which kinetic energy is transferred to the last ball—this illustrates the speed of sound propagation. However, the slower free movement of the outer balls is clearly visible. Their initial speed is proportional to the force applied to the opposite ball, and this illustrates the speed of air molecule movement, which is proportional to the acoustic pressure or the strength of the initiating impulse.

Once Again: The Speed of Sound Propagation

Now that we understand the mechanism of sound propagation, it becomes clear that the speed of sound is proportional to the volumetric density of air particles. When particles are in an equilibrium state and physically closer together, collisions occur more quickly, allowing the acoustic impulse to propagate faster.

This explains why in colder air, where air particles have lower kinetic energy and are therefore closer to one another, the speed of sound is actually higher.

For example:

• At 20 °C, the speed of sound is 343 m/s

• At 40 °C, it decreases to 335 m/s

Why Does the Sound Impulse Propagate Through Space?

This stems from the principle of energy conservation.
The total amount of energy in a system remains constant; only its form can change—for example, from kinetic energy to heat. A fundamental property of energy is that it cannot disappear, nor can it change form in an infinitely short moment.

Consider this analogy:
A large meteor crashes into the Earth and explodes, even though it contains no explosives. The sudden release of energy is a consequence of the kinetic energy it carried—not of any internal charge.

When an air particle receives kinetic energy, it must respond in some way. It may:

• share part of its energy with a neighboring particle,

• begin vibrating in place,

• start rotating.

The same happens to the impacted particle: it receives part of the kinetic energy, is pushed forward in space, and then passes some of that energy to yet another neighboring particle, and so on.

This chain of energy transfer—one particle imparting energy to the next—is what causes a sound impulse, or energetic disturbance, to propagate through space.
In this way, sound propagation is always inseparably linked to the transmission of energy.

What Exactly Is a Wave?

A wave is a propagating dynamic disturbance—a deviation from equilibrium (such as the impulse described earlier)—in one or more physical quantities. The propagation of a wave through space is always inherently linked to the transport of energy. For example, when two galaxies collide, a gravitational wave is generated as a dynamic disturbance in spacetime. This wave carries with it a fraction of the energy derived from the galaxies’ kinetic energy.

There are many types of waves. As we’ve already discussed, sound is a mechanical wave, a disturbance in the equilibrium of atmospheric pressure, and we have described the mechanism by which it propagates through a medium such as air.

The propagation of electromagnetic waves is described by Maxwell’s equations, which, in simplified terms, can be viewed as periodic electromagnetic induction.

The propagation of gravitational waves in spacetime, predicted by Einstein, is explained through his General Theory of Relativity.

Waves as Information Carriers

Besides transporting energy, waves can also carry information—provided they are intentionally modulated during their generation by converting another form of energy. For example, an emergency electronic warning device converts electrical energy into a periodic acoustic impulse that is modulated with specific information for public safety.

It is important to understand that during the propagation of a sound wave, air particles do not travel with the wave—they merely oscillate in place. What actually travels through the medium is the periodic impulse, not the particles themselves.

Another important note: a sound wave is a longitudinal wave, meaning the particles that facilitate its transmission oscillate locally, both in the same direction and opposite to the direction of wave travel. However, on a larger scale, those particles remain essentially in place.

A Side Note: The Role of Quantum Theory

Although the basic mechanisms of sound propagation can be explained using classical mechanics, quantum theory introduces additional nuances—particularly when examining molecular behavior at the microscopic level. Quantum effects can influence molecular vibrations and energy states, which in turn may affect certain acoustic properties.

To Conclude, One More Fascinating Aspect: The Dynamics of Perceived Sound Loudness

The human ear possesses an incredible dynamic range—the ability to perceive an enormous spectrum of acoustic pressure values. As mentioned in the first part of this article, the ear can detect dynamic changes ranging from 0.000000020% to 0.1% of atmospheric pressure. Expressed as a ratio, that amounts to a factor of five million. To work effectively with such an immense numerical range—and to maintain the same resolution across the entire scale—we need a special approach.

Interestingly, this need did not arise from acoustics. It was John Napier, in the 17th century, who first tackled the challenge. He developed a method that allowed easier manipulation of large numbers while preserving relative accuracy—that is, maintaining consistent precision across a wide span of values. His solution was the introduction of the logarithmic function.

 One Equation Won’t Hurt:

Thanks to this mathematical breakthrough, we now express acoustic pressure—SPL (Sound Pressure Level)—using a logarithmic function, measured in decibels (dB):

SPL (in dB) = 20 × log₁₀ (p / p₀)

where:

• p is the measured sound pressure

• p₀ is the reference sound pressure (typically 20 μPa in air)

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