fluctuating sound

Otokun

After learning about the "Singing Dragon," I tried to find places around school that made a similar sound. It wasn't quite as impressive as the Singing Dragon in Nikko, but there were a few places where clapping my hands against parallel walls produced the same buzzing sound.

father

Besides the space around the walls and ceiling, one condition that allows you to hear it well is whether it's a quiet place. The phenomenon of "singing dragons" is caused by reflected sound that continues for a long time at regular intervals, but in a quiet place with little other noise, you can hear the attenuating reflected sound until it disappears.

Otokun

That's right. If you go early in the morning, you might be able to find the location of the "singing dragon" that you couldn't hear during the day.
Right. We've found it in several places so far, but the rough, beeping sound was different depending on the location.

father

"You've probably heard sample sounds before where the sense of fluctuation or roughness became more pronounced depending on how many times a continuous sound changed per second (modulation frequency)."

Otokun

So, the time period of reflected sound differs depending on the location, which means it sounds different?

father

That's right. Don't you think it would be great if we could quantify the feeling we get when we hear something?

Otokun

Is that not what you meant by decibels, like you explained before?

father

Decibels? Yes, dB is a level expressed as a ratio to a certain standard. Quantitative values like loudness can be represented by levels, but quantifying how something sounds is is extremely difficult. However, there are ways to quantify a single sensory quantity, such as the sense of fluctuation in sound or the roughness you've experienced before.

Otokun

That sounds interesting. Can you tell me more?

father

Actually, I put the sound of the crying dragon from the other day through a certain analysis.
img-fluctuating-noise-01
Take a look at this diagram. I won't go into detail, but in this diagram, the horizontal axis represents the pitch (frequency) of the sound, and the vertical axis represents the modulation frequency. The color represents the magnitude of the fluctuation. If you focus on the modulation frequency in particular, it shows that 30 Hz is the frequency at which the fluctuation is most pronounced. In a paper published in 1965, before the fire, which explained the phenomenon of the "singing dragon," there was a description of "29 reflected sounds per second," and this analysis proves that very point.

Otokun

So, sound can be analyzed not only by level and frequency, but also by methods like this.

father

That's right. My dad was also interested in this analysis and tried it with other sounds. One interesting one, which you probably don't know, is the "sawari" of the shamisen.

Otokun

Sawari? I don't know much about the shamisen, but what exactly is "sawari"?

father

The shamisen has three strings, but the lowest-pitched string, the first string, is not passed through the nut (called the upper bridge) on a guitar. Instead, the string lightly touches the neck, producing a buzzing, noise-like sound. This is a characteristic of the shamisen, and this sound is essential to the instrument.

Otokun

I get it! You analyzed that "beep" sound, right?

father

That's right. The figure below (Figure 1) shows the result, and you can see that the fluctuation component is large around the modulation frequency of 140 Hz. Also, the figure below (Figure 2) is a time waveform, and as you might expect, there are 14 pulses in 0.1 seconds. I have a sound file, so listen to it.

Otokun

Oh, really?

father

The shamisen's sound also has a large bandwidth in the 1kHz range, but because the modulation frequencies are close, it can be perceived as having a similar muddy, rough sound.

Otokun

In what other situations can this analysis method be used?

father

Yeah, I think it could be useful for evaluating the sounds of machinery. Machines usually rotate at a constant speed or move up and down, which will generate sounds that fluctuate over time. For example, if the interior panels of a car rattle, it often becomes a complaint because it's considered an abnormal noise. Apparently, there have been cases where it has been used to extract such abnormal noises.

Otokun

It makes you want to try out different motor sounds, air conditioner sounds, and so on.

father

That's right. I hope it helps to make the sound more pleasant.