Sound hum

When you tune a guitar, you adjust the tuning peg on the string you're tuning until the beat between the two notes disappears, right? Why does that beat occur?

Ah, guitar tuning. Nowadays, we have tuners, so we don't tune our guitars that way as much anymore. A beat is the interference of sounds with slightly different frequencies, and the difference in those frequencies is what creates the fluctuating frequency.

What does it mean that a difference in frequency becomes a fluctuating frequency?

Take a look at this diagram (below). Waveform A represents a 200 Hz sound, and waveform B represents a 205 Hz sound. Let's listen to these two sounds first.

Wow. I can clearly hear the growl.

That's right. The sound you're hearing now is fluctuating 5 times per second. In other words, the fluctuation frequency is 5 Hz, which is the difference between the frequencies of the two sounds.

But why?

Figure 2 is a magnified view of this section. Look at waveforms A and B at the point where the amplitude of the superimposed waveforms becomes zero.

Waveform A has its maximum value on the positive side, and waveform B has its minimum value on the negative side. Since they are the same value but one is positive and the other negative, do they cancel each other out and become 0?

That's right. But when that happens periodically, it creates a beat.

Why does this happen periodically...?

The ratio of the difference between 200 Hz and 205 Hz, which is 5 Hz, to 200 Hz is 40. Therefore, every 40 waves, it looks like this diagram, and the sum of the amplitudes of the waves becomes ±0.

I see. That reminds me of the fluctuating sounds you told me about when we were talking about the "crying dragon."

That's right. It's related. Next time, I'll explain the characteristic phenomena that occur under certain conditions when the frequencies of two sounds are far apart.