2. Sound Pressure - Loudness and Level

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 and 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 to start our discussion on loudness. What is pressure then? You can think of it as a force that is responsible for displacing the molecules

then? You can think of it as a force that is responsible for displacing the molecules of air in a cross sectional area of space. You’ve got to remember that, this isn't the wind we are talking about. There is no movement of a mass of air particles with sound.

Sound is just a localized fluctuation or disturbance of the pressure of a fluid, like air. And

this disturbance is propagated at the speed of sound, outwards in all directions. Going

by this definition, there is a need for the pressure of the medium to already exist, before sound can propagate through it. What is that? It’s the pressure exerted by the air around you. The glorious atmosphere of the earth, a whole 100 kilometers of voluminous air pushing

you. The glorious atmosphere of the earth, a whole 100 kilometers of voluminous air pushing down against us and the earth’s surface, constantly, without a break, with a force of about 101325 N against each square meter measured at sea level. We can also say that

the atmosphere exerts a pressure of 101325 Pascal on us, Pascal being the SI unit or the standard unit of measure of pressure. 101000 Pa. Is that a lot? Doesn’t seem like it. We don’t feel constantly pressured by the atmosphere, that’s because we’ve evolved

it. We don’t feel constantly pressured by the atmosphere, that’s because we’ve evolved to withstand this constant atmospheric pressure that virtually hasn’t changed much over the course of history. This predictable atmosphere that we live under has helped develop unique adaptations in the human body, especially the ear, which is capable of perceiving even

the slightest changes in pressure, several orders of magnitude lower than the equilibrium.

And we’ll find out soon enough that we cannot tolerate even relatively small changes of pressure in a short duration of time.

Instead of thinking about sound pressure waves on their own, we can think about them as being superimposed on top of the constant and static atmospheric pressure, oscillating around the equilibrium. A typical question you could ask now, is what’s the pressure values of

equilibrium. A typical question you could ask now, is what’s the pressure values of sounds we normally hear? A normal conversation with a friend observed from a distance of 1m is around 2 mPa. The key point to note is that distance from the source plays a very

important role in determining pressure. If you are right up against the source, it’s perceived louder since the pressure is higher, as opposed to say, 10m 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. 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 a 60 micro pascal. The lowest

micro Pascal. The sound of your own breathing is as low as a 60 micro pascal. The lowest

audible sound that a good pair of undamaged ears can hear is well established to be around 20 micro Pascal, for a 1kHz pure sine tone played next to our ears. For a limited range of higher frequencies we can hear sounds at much lower pressure than this, but that’s a topic for another day, and we’ll sound that horn when we get to Loudness perception.

But for a majority of us, we can’t perceive sounds this low. It’s 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. Pause this video for a bit and try to listen

to your own natural breathing, without forcing it. Unless you’re in an extremely quiet environment, you can’t. You probably would’ve heard your own breathing in the dead of the night when you’re 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, 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 it’s pressure component below the noise floor is imperceptible

floor. Any source of sound with it’s pressure component below the noise floor is imperceptible to our ears. It’s effects are masked and it’s never heard. Naturally, the measurements made for the threshold of hearing, of 20 uPa is made in a controlled environment, in rooms

that are designed to be completely soundproof from the outside and non-reflective from the inside, called anechoic chambers.

If 20 uPa is the threshold of human hearing, let’s see what the other end of the spectrum is like? The sound of traffic on a busy road 10m away registers at around 0.2 Pa. The sound

is like? The sound of traffic on a busy road 10m away registers at around 0.2 Pa. The sound

of a jackhammer on a construction site a meter away is around 2 P. We’re already past the point where the loudness isn’t just an annoyance anymore, it’s downright dangerous for prolonged periods of exposure. You remember the Vuvuzelas? These demonic devices used in unison in sporting

events. They register at around 20 Pa, at a meter away. Imagine the loudest scream you’ve

events. They register at around 20 Pa, at a meter away. Imagine the loudest scream you’ve ever heard. Now imagine that an inch away from your ears. That’s around 100 Pa, and

ever heard. Now imagine that an inch away from your ears. That’s around 100 Pa, and we’ve reached what’s known as the threshold of pain, where the stimulus of sound starts to result in a perception that is physically painful. At these levels, even short bursts of exposure could result in hearing damage and even permanent hearing loss. Discussing

anything above this is not incredibly useful for sound engineers. But it is interesting to find out what happens as we approach the atmospheric pressure. As the pressure mounts up, sustaining a pressure disturbance requires an immense amount of energy. But short instantaneous bursts of pressure variance are easy enough to create, for example, popping a balloon

right next to your ear could result in a staggering 1000 Pascal of pressure disturbance, so never try that at home. As the pressure difference increases, the compression phase of pressure waves starts to build up in temperature and this temperature gradient follows along with the wave. The heat is not transferred to the fluid, since the sound waves are adiabatic

the wave. The heat is not transferred to the fluid, since the sound waves are adiabatic in nature and there just isn’t enough time for heat transfer to take place. The loudest

sustained sound that’s physically possible is a mean deviation of the atmospheric pressure itself of 101325 Pa at sea level, at which point the wave swings from near vacuum to 2atm of pressure. Beyond this, the pressure wave is no longer a sound wave, but rather

a shock wave. That’s because the rarefactions of sound waves cannot be lower in pressure than vacuum, and the extra energy in the system distorts the wave violently, and creates a non-linear wave where you have extra build up of compression pressure. These waves are quite dangerous and violent, as they carry a pressure front which is incredibly hot and

high in pressure, followed by an immediate drop in pressure and a suction pull towards the source.

That was a bit of trivia, but let’s not get bogged down by what high explosives are capable of generating, Let’s instead talk about what our instruments and devices are capable of producing. For all audio related measurements, the range can be limited from the threshold of human hearing, which is about 20 uPa, to the threshold of pain, which is

around 100 Pa. That’s an order of magnitude around 6 times higher, and therein lies the problem. Representing this vast range of pressure values on a linear scale can get cumbersome,

problem. Representing this vast range of pressure values on a linear scale can get cumbersome, and you lose a lot of resolution at low pressure values. In the next video we’ll look at how a logarithmic scale is better suited to represent this range of data, and more specifically the decibel scale used for measuring the sound pressure level.