There's life above 20000 Hertz!

Actually, we all knew this already (at least those of us who work with digital audio), but since we humanoids can only hear up to about 20,000 Hertz (and only if we're 10 years old and have clean ears), we often don't think about it.

And so, when about 30 years ago, equipped with a sound card and a microphone capable of capturing sound with a bandwidth greater than 22,000 Hz, James Boik of Caltech analyzed the spectrum of some musical instruments and discovered frequencies above 50,000 Hertz, everyone was amazed.

A few words of explanation for the uninitiated. The frequency range normally reproduced in digital audio ranges from 0 to 22,050 Hz for CDs and 24,000 Hz for DVDs. Which, considering that humanoids hear up to about 20,000 Hz as children and lose high frequencies as they grow (the average 70-year-old doesn't reach 15,000 Hz), is fine.

Now, to record audio that reaches 20,000 Hz, a digital audio device must operate at a much higher frequency. To be precise, at least double. So, to record a sound that we consider very high-pitched at 20,000 Hz, a sound card must operate at at least 40,000 Hz. This means it must process at least 40,000 numbers per second for each audio channel (80,000 for a stereo signal, 200,000 for a 5+1).

It's a similar situation to that of cinema. A film is nothing more than a sequence of photographs, i.e., still images. To get the sensation of movement, we need to overcome a threshold beyond which our eye-brain system is no longer able to perceive individual images, but each one merges with the next, giving the illusion of movement. For sight, this threshold is about 25 images per second (this is the frequency of PAL, or European television; the American NTSC standard, however, is just under 30). However, it has been observed that with higher frequencies, the image is sharper and the quality is superior, especially in the case of large screens. Therefore, cinema uses frequencies around 50/60 Hz, as do computer monitors and digital TVs nowadays.

Let's get back to the audio. The truth is that, if we consider that the highest C on a piano emits a note whose fundamental is 4186 Hz (tuned to A at 440), it's enough to reach the fifth harmonic component to exceed 20,000 Hz, and there are far more than five harmonics. Consequently, we all knew that the spectral range of high notes on musical instruments exceeded the fateful threshold of our perceptual system, but no one imagined that it could also happen with notes that were not that high.

And yet, Boik's research shows, for example, that a trumpet playing a Bb with a fundamental of 465.4 Hz emits harmonic components that exceed 50 kHz, passing the 100th harmonic with an amplitude that is, yes, low, but not exactly trivial.

Click on the figure below to enlarge it and read the caption. The full article is here or here.

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