Acoustic pressure is the variation in pressure that occurs in a medium (such as air or water) when a sound wave propagates through it.
Physically, it is the difference between static atmospheric pressure (the normal air pressure when there is no sound) and the total instantaneous pressure generated by the sound wave as it passes. This variation occurs due to the compressions (increase in pressure) and rarefactions (decrease in pressure) of the particles in the medium as sound energy travels through it.
If you imagine the graph of a sound wave, amplitude is represented as the distance between the equilibrium point and the highest point (crest) or the lowest point (trough) of the wave. Technically, it is the distance between the point of maximum compression and maximum rarefaction of the air.
The formula that defines it is:
- \( p(t) \) is the instantaneous acoustic pressure (pressure variation relative to \( P_0 \)).
- \( P_{\mathrm{tot}}(t) \) is the total pressure at a specific moment.
- \( P_0 \) is standard atmospheric pressure (typically \( 101\,325 \, \mathrm{Pa} \)).
Measurement of acoustic pressure
The official unit of acoustic pressure is the pascal (Pa). However, the human ear has such a wide range of perception that measuring it solely in pascals would be impractical:
- Threshold of hearing: The faintest sound we can hear is only about 20 µPa (micropascals).
- Threshold of pain: The sound level that begins to cause physical damage is about 20 Pa.
Because the threshold of pain is one million times greater than the threshold of hearing, the logarithmic decibel scale (dB SPL) is commonly used to make these values more manageable.
Factors that determine it
The amount of acoustic pressure you perceive depends on several elements:
The sound source
The pressure generated depends directly on the physical and operational characteristics of the object producing the sound. It can be divided into three aspects:
- Size: Large sources (such as a large loudspeaker or an industrial engine) have the ability to move a greater volume of air, which results in higher acoustic energy and pressure generation.
- Power: There is a direct relationship between power (energy emitted per second) and pressure. A higher-powered device, such as a high-end amplifier, will necessarily produce stronger pressure variations in the air.
- Directivity: Determines how energy is distributed in space. Directional sources (such as a tweeter) concentrate energy in a specific area, increasing pressure in that zone. In contrast, omnidirectional sources disperse sound in all directions, reducing pressure concentration at any given point.
Distance from the source
Acoustic pressure does not remain constant; it decreases as the listener or measuring device moves away from the source.
According to the inverse square law, as distance increases, sound energy must spread over a progressively larger area. Each time the distance is doubled from the sound source, acoustic pressure is reduced by half.
In terms of sound pressure level, this corresponds to a drop of approximately 6 dB SPL.
The propagation medium
The properties of the material (air, water, solids) through which the sound wave travels significantly affect pressure.
Density is the determining factor. In denser media, such as water, particles are closer together, allowing energy to transfer more efficiently. This means that sound travels not only faster but also with greater acoustic pressure.
Another factor is dispersion. In less dense media, such as air, waves encounter less resistance to spreading out, causing energy to disperse more quickly and pressure to decrease more easily compared to liquid or solid media.
Difference between acoustic pressure and sound intensity
Although they are closely related, acoustic pressure and sound intensity measure different aspects of a sound wave.
- Acoustic pressure: Reflects the physical variations or pressure fluctuations that the sound wave produces in the particles of the medium (such as air) as it propagates. Essentially, it is the difference between normal atmospheric pressure and the pressure generated by the sound.
- Sound intensity: Measures the amount of energy transported by the sound wave per unit area. Rather than focusing solely on pressure change, it considers how much energy flows through a given space.
Both quantities are connected by a physical formula showing that intensity is proportional to the square of pressure:
In this relationship, \( p \) is acoustic pressure, \( \rho \) is the density of the medium, and \( c \) is the speed of sound. This means that if acoustic pressure increases, sound intensity will also increase but quadratically.