パスカルとデシベル

Oto-kun

Today at school, it seems that a neighbor complained about the noise from the broadcast in the schoolyard, saying it was "loud." The noise level was 60 dB. My father had mentioned 60 dB when he explained reverberation time before, right? At that time, I thought I understood it somewhat, but now I'm not sure if the meaning of 60 dB is different in this case.

father

I see, I didn't explain to you what decibels are as a unit. So, let's go back to the beginning and I'll teach you how sound is generated and how its energy is measured.

Oto-kun

Dad, you taught me a long time ago that sound is the vibration of air.

father

That's right. To be more precise, the average air pressure is called atmospheric pressure, and when there are areas of higher and lower pressure than this atmospheric pressure, they propagate as waves, which is what we perceive as "sound." For example, when you tap a desk, it produces sound because the desk's vibrations cause the air to vibrate, creating areas of high and low atmospheric pressure.

Oto-kun

But, I don't really understand why air vibrates.

father

Have you ever done an experiment with a spring scale in your science class? Imagine a weight hanging from the spring scale. When you pull the weight and let go, the spring and the weight vibrate up and down, right? For this vibration to occur, both the spring and the weight are necessary. For example, in the case of a guitar string, the property of the string trying to return to its original position when plucked acts like the 'spring', and the weight of the string itself corresponds to the mass, or 'weight'.

Oto-kun

It is understood that a spring and a weight are necessary for the vibration of an object, but does air also vibrate like a spring and weight?

father

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

Oto-kun

I see, so when fanning with a hand fan, the resistance I feel might be due to the weight of the air.

father

That's right, air has the properties of a 'spring' and 'mass', which allows it to vibrate. And sound travels through the air.

Oto-kun

But I still don't quite understand why sound is transmitted when it vibrates.

father

When you hit the table and it vibrates, think of the surrounding air being pushed. This pushed air becomes dense, creating areas of higher pressure than the surrounding air. That area pushes the neighboring air, and the pushed air increases in pressure, pushing the next air over... and so on, repeating like a domino effect, allowing sound to travel.

Oto-kun

I finally understood that sound is a vibration in the air.

father

Thus, when sound travels, there will be areas of high pressure and low pressure. This change in pressure is called 'sound pressure.' The unit is pascal (Pa).

Oto-kun

Isn't the unit of sound in decibels? What you've taught me so far, Dad, has been in decibels, right?

father

Decibels are a unit that allows us to handle sound pressure levels in a convenient range of 2 to 3 digits. The reference sound pressure is set at 20 microPascals (μPa), which is approximately the same as the minimum sound pressure that humans can hear. Since 1 atmosphere is about 100,000 Pascals, this means a change of 2 out of 10 billion of 1 atmosphere, which is a very small change.

Oto-kun

Why can it be expressed in 2 to 3 digit numbers?

father

The smallest sound pressure of 20 microPascals means 20 Pascals out of a million, and a deafening loud sound is about 20 Pascals. This means that when expressed in Pascals, we are dealing with a range of 1 million times in sound pressure, which is quite inconvenient. You might learn this in high school math, but decibels are expressed using logarithms. The sound pressure level is expressed as the logarithm of the square of the ratio of a sound's pressure P to a reference sound pressure.

Oto-kun

I don't really understand it well, but the sound pressure level is a convenient unit that expresses a range of one million in two to three digits.

father

In 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 at 120 dB is 20 Pascals in terms of pressure, which is about 20 out of 100,000 of one atmosphere, indicating that even loud sounds are just tiny vibrations in the air.

Oto-kun

Just wondering, what's the difference between reverberation time at 60 dB and noise level at 60 dB?

father

The reverberation time of 60 dB is a relative measure. For example, if there is sound in a space with a sound pressure level of 100 dB, even after the sound stops, the sound that reflects off the walls and ceiling remains, gradually fading away. The time it takes for the sound to decay to 60 dB (which is one-thousandth of the sound pressure) is what we refer to as reverberation time, meaning the time until the sound pressure level in the space drops to 40 dB. The noise level is defined based on how human hearing is less sensitive to low frequencies and more sensitive to higher frequencies around 2 kHz, resulting in an adjusted sound pressure level known as the noise level, which in this case was 60 dBA. I will explain more about noise levels next time.