Pascals and decibels

Otokun

Apparently, someone living nearby complained today that the sound of the school's public address system playing in the schoolyard was too loud. The noise level was 60 dB. Dad mentioned 60 dB when he explained reverberation time to me before, right? I thought I kind of understood it then, but now I'm kind of confused, wondering if the meaning of 60 dB is different in different contexts.

father

Oh, right, I haven't explained to Oto what a decibel is. So, let's go back to the beginning and I'll explain why sound is produced and what units are used to measure its energy.

Otokun

Dad, you taught me a long time ago that sound is vibration in the air, right?

father

That's right. To be more precise, atmospheric pressure is the average pressure of the air, and areas with higher and lower pressures than that atmospheric pressure are created, and when these waves are transmitted, that's what we call "sound." When you tap on a table, it makes a sound, right? That's because the vibration of the table vibrates the air, creating areas of high and low atmospheric pressure.

Otokun

But I still don't really understand why the air vibrates.

father

Oto, you've probably done an experiment with a spring scale in science class, right? Imagine a spring scale with a weight hanging from it. If you pull the weight and then release it, the spring and the weight will vibrate up and down. You need a spring and a weight for vibration to occur. For example, in the case of a guitar string, the property of the string to return to its original shape after being plucked is the "spring," and the weight of the string itself corresponds to the mass, or "weight," right?

Otokun

I understand that springs and weights are necessary for an object to vibrate, but can air also vibrate like a spring and weight?

father

That's right, when you press on a ball, it springs back and tries to return to its original shape. Air also has spring-like properties. In addition, air has weight. Balloons float because the hydrogen or helium filled inside is lighter than air.

Otokun

I see, that makes sense. When you fan yourself with a hand fan, the resistance you feel is probably due to the weight of the air.

father

That's right, air has the properties of both a "spring" and "mass," so it can vibrate. And sound travels through the air.

Otokun

But I still don't quite understand why vibrations transmit sound.

father

Imagine tapping on a desk and causing it to vibrate; the air around it is compressed. This compressed air becomes denser, creating areas of higher pressure. These areas then push the surrounding air, which in turn increases in pressure, pushing the next area, and so on—like a domino effect, repeating as sound is transmitted.

Otokun

I finally understand. Sound is vibration in the air.

father

When sound travels, areas of high and low pressure are created. This change in pressure is called "sound pressure," and its unit is the pascal (Pa).

Otokun

Isn't the unit of sound decibels? Dad has always taught me about decibels, right?

father

The decibel is a unit that allows us to handle sound pressure with a convenient number of orders of magnitude, typically two to three. The standard for sound pressure is set at 20 micropascals (μPa), which is roughly the same as the minimum sound pressure that humans can hear. Since 1 atmosphere is approximately 100,000 pascals, this represents a tiny change of 2/10 billionth of 1 atmosphere.

Otokun

How can that be represented by a two- or three-digit number?

father

The smallest sound, 20 micropascals, means 20 parts per million of a pascal, and a deafeningly loud sound is probably around 20 pascals. So, expressing it in pascals means dealing with a range of 1 million times the sound pressure, which is quite inconvenient. You probably learned this in high school math, but decibels are expressed using logarithms. The sound pressure level is expressed by taking the logarithm of the square of the ratio of the sound pressure P of a given sound to the sound pressure of a reference. .....See formula below *1

Otokun

I don't really understand it, but it seems that sound pressure level is a convenient unit that expresses a range of 1 million using two or three digits.

father

According to this formula, a tenfold increase in sound pressure corresponds to a sound pressure level of 20 dB, and a millionfold increase in sound pressure corresponds to a sound pressure level of 120 dB. A loud sound of 120 dB corresponds to a pressure of 20 Pascals, which is about 20/100,000th of an atmosphere, so you can see that even a loud sound is just a tiny vibration of air.

Otokun

I kind of understand. What's the difference between a 60 dB reverberation time and a 60 dB noise level?

father

The 60 dB reverberation time is a relative quantity. For example, suppose there is a sound in a space with a sound pressure level of 100 dB. Even if you stop the sound, some of the sound will remain reflected off the walls and ceiling of the space, and it will gradually fade away. The reverberation time is the time it takes for the sound to decay by 60 dB (one-thousandth of the sound pressure) during this fading process. In this case, the time it takes for the sound pressure level of the space to become 40 dB is called the reverberation time. The noise level is the sound pressure level after frequency correction, because human hearing is insensitive to low sounds and sensitive to high sounds around 2 kHz. In this case, the noise level was 60 dBA (*2). I'll explain noise levels in more detail next time.