Sound Pressure

🎯 Learning Objectives:

In this topic, we will look at pressure from the lens of loudness. We start with pressure, since our ears are receptive to changes in air pressure, and is quite easy to measure. We will look at the SI unit of pressure, Pascal, and the vast range of sound values that it can represent, all the way from the quietest (threshold of hearing) to the loudest (threshold of pain) sound that a human ear is capable of hearing. We will also discuss pressure values of sounds higher than that when sound morphs into shock waves at the fringe of the atmospheric pressure. But more importantly, the topic sets up the discussion to talk about how to represent such a vast range of values. When a linear scale fails to give us appropriate resolution, we turn towards a logarithmic scale.

📘 Sound is a pressure wave pressure at any given region is quite easy to measure. In fact a microphone does it all. The time our ears are receptive to changes in pressure on this tiny modulation of air pressure next to our ear is what is translated as sound. So pressure is as good a place as any other to start our discussion on loudness.

What is pressure?

Let us watch the video lecture to understand it more interactively.

You could ask now is what is the pressure values of sound we would normally hear. A normal conversation with a friend observed from a distance of about 1 meter is about 2mPa. The key point to note here is the distance from this source plays a very important role in determining pressure. If you are right up against the source it is perceived louder since pressure is higher as opposed to say 10 meters away. The relationship between pressure and distance is given by the inverse distance law which states that the pressure is inversely proportional to the distance from the source.

Here $d$ is the distance

So as you move away from the source, the pressure decreases linearly. The second point to note is how low the pressure value is when compared to the atmospheric pressure. We can go much lower though a calm room with the air conditioning on would be around 600 micro Pascal. The sound of your own breathing is as low as 60 μPa. The lowest audible sound that a good pair of undamaged ears can hear is well established to be around 20 μPa for a one Hz pure sine tone played right next to our ears. For a limited range of higher frequencies we can actually hear sounds at a much lower pressure than this. For the majority of us we cannot perceive sounds this low. It is not because our ears are incapable of it, but just because we are surrounded by ambient noise from everywhere which drowns out everything lower in pressure.
Here is the chart showing the different pressure values of the sound

Try to listen to your own natural breathing without forcing it unless you are in an extremely quiet environment. You cannot. You probably would have heard your own breathing in the dead of the night when you are in bed but during the day you are bombarded with ambient noise from the cooling fan of your laptop, the temperature control unit in your home, the wind noise outside or traffic noise at a distance. These sources of sound combined together make up a noise floor. Any source of sound with its pressure component below the noise floor is imperceptible to our ears. Its effects are masked and it is never heard naturally.

It is interesting to find out what happens as we approach the atmospheric pressure. Let see the video lecture about this with animation.

📝 Key Takeaways

• Sound is essentially a pressure wave, and our ears detect tiny variations in air pressure.
• Pressure is measured in Pascals (Pa), with typical sound pressures ranging from extremely quiet (~20 μPa) to extremely loud (~100 Pa, near the threshold of pain).
• The perceived loudness of a sound depends on both its pressure and the distance from the source.
• Pressure decreases with distance according to the inverse distance law:
  $$p ∝ \frac{1}{d}$$
• Normal environmental sounds, such as ambient noise, form a noise floor that masks sounds with pressure below it.
• The range of audible pressures is extremely small compared to atmospheric pressure, making quiet sounds like breathing nearly imperceptible in daily life.
• For very high-pressure sounds, pressures can exceed normal audible ranges and transition into shock waves at extreme levels.
• Linear scales are insufficient to represent the vast range of audible pressures; logarithmic scales are used to provide better resolution for human perception.
• Understanding pressure is fundamental for discussing loudness and the measurement of audio signals in both objective and perceptual terms.

🧪 Interactive Demo

Distance & Pressure Simulation

🧠 Quick Quiz

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