octave

Otokun

Dad, the other day when you were telling me about Pascal and decibels, you told me that the unit for noise level is dBA, right? Today, when I was waiting for the bus at the station, there was a display on a tower in the green space in front of the station that showed the current noise level in dB. I thought that since it was a noise level, it would be A-weighted like you told me, but there was no A on the display.

father

The term "noise level" likely refers to A-weighted sound pressure level, which is probably why the "A" was omitted. Most people would probably think of decibels as a unit of sound, but the "A" might make them wonder what it means. In the past, the unit "hon" was also used, but it was standardized to dBA in 1997. The term "noise level" is unique to Japan; the correct term is "A-weighted frequency-weighted sound pressure level."

Otokun

That's a long name, hard to remember. "Noise level" is much easier to understand.

father

Noise levels are actually very useful. Most noises have complex frequency components ranging from high to low pitches, and their volume increases and decreases over time. The fact that we can evaluate the human response to such complex noise with a single numerical value is amazing.

Otokun

You taught me a while ago that human sound perception involves frequency masking and temporal masking, right? Does noise level also take those effects into account?

father

That's not quite right. There's a quantity called "loudness" that represents the loudness of a sound, and this loudness takes masking into account, accurately capturing the loudness of sounds that humans hear. However, the calculations for it are complex, and there aren't many measuring instruments for it yet. Recently, loudness has started to be used for evaluating noise generated by machines, such as office equipment and the sounds inside cars, but road traffic noise is often evaluated using noise levels.

Otokun

Why is that?

father

When a machine is malfunctioning, you can often tell by the sound it makes. These abnormal sounds are called "abnormal noises," but evaluating them using noise levels often doesn't accurately reflect how humans perceive the sound. This is because abnormal noises often have a dominant frequency, so considering frequency masking allows us to represent the perceived loudness more accurately. Conversely, road traffic noise, which encompasses a wide range of frequencies, can be evaluated using noise levels.

Otokun

Is it a frequency range? The method of evaluation needs to be determined by the type of noise.

father

That's right, I remember explaining how the basilar membrane vibrates inside the cochlea when we talked about frequency masking. Human hearing is roughly A-weighted, but it actually has a filter to distinguish between high and low pitches. The bandwidth of that filter is called the critical band, and it's roughly 1/3 of an octave wide.

Otokun

??? I don't really understand. First of all, human hearing has a filter that allows us to distinguish between high and low pitches. ...1/3 octave? ...What does that mean?

Otokun

Which note on a guitar corresponds to 440 Hz?

father

That's the note on the 5th fret of the 1st string. On a guitar, one fret is a semitone, so the next note, A, is on the 17th fret of the 1st string. So, a semitone is 12, and an octave is 1/12 of an octave. On a piano keyboard, adjacent notes, including the black keys, are a semitone, so they are also 1/12 of an octave apart.

Otokun

So, a third octave is four semitones, which is two whole tones, so it's the interval between C and E, right?

father

That's right. An octave is a doubling of frequency, but for sound analysis, instead of using do-re-mi, a round number of center frequencies based on 1000 Hz is used. Like 63 Hz, 125 Hz, 250 Hz, 500 Hz, 1000 Hz, 2000 Hz, 4000 Hz, 8000 Hz, and so on. I told you before that humans can hear sounds from about 20 Hz to 20 kHz. But the sounds that exist in our living spaces are generally between 63 and 8000 Hz, so it's common to evaluate them using these 8 bands or so.

Otokun

What's a band?

father

Oh right, I haven't talked about bands yet. An octave band is a frequency range with a width of one octave. The formula is complicated, so...
Without going into too much detail, an octave band with a center frequency of 1000 Hz has a frequency range of 770 to 1410 Hz, and an octave band with a center frequency of 500 Hz has a frequency range of 355 to 710 Hz. The level of sound intensity contained within one octave is called the octave band level. When analyzing sound, the easiest and most general approach is to evaluate it using a single number, such as dBA, for noise level. However, with noise level alone, you can't tell whether the noise is mainly low-frequency sounds or high-frequency sounds. Therefore, by analyzing using octave bands, or even more precisely, 1/3 octave bands, you can capture the frequency characteristics of the noise.

Otokun

But why is such an analysis necessary? If there are no unusual noises, can't we evaluate it based on the noise level?

father

Consider taking measures to mitigate noise. Knowing the noise levels for each frequency will help you determine which frequencies need to be addressed. For example, when measuring road noise, if you have not only the noise level but also the octave band measurements, you can estimate how to design a sound barrier to achieve the optimal design, and also what the noise level will be like in living spaces such as houses near that road.

Otokun

I see. Noise levels are sufficient for evaluation, but when considering countermeasures and predictions, octave band analysis is effective.