Resonant Frequencies

Every physical system has a resonant frequency.

© 2021 Janette Keene Taylor

Spending some time in Bandon, Oregon, I find myself contemplating the nature of dynamic systems. I’m looking over the beautiful rocky coast and I watch in awe as the waves break against the wondrous jutting rock outcroppings of this rugged shore. Sitting quietly and counting the waves, I think about dynamic systems from the very tiny, such as the quartz movement of my watch, to the massive impenetrable glory of the ocean, a colossal system the frequency of which may be observed at its edge as waves.

Every object has a resonant frequency and all sorts of things display a useful resonant frequency. The word oscillation is used to indicate a periodic recurring event, whether referring to the body of a brass bell when struck, or a quartz crystal in a watch which issues evenly spaced electrical pulses defining the seconds and minutes. The bell rings (oscillates) at a tone defined by its resonant frequency. It issues a particular musical note, and no matter how hard you strike the bell, it may be louder or quieter but its tone (its frequency) remains the same. The same is true for a quartz crystal, a bowl of gelatin and a swinging pendulum. They each have a resonant frequency and we humans use resonant frequencies for lots of practical things.

With all of that out of the way, I’ll explain what the resonant frequency actually is. It is that frequency at which the system may oscillate with a minimum of required power. It relates to how that system absorbs and then releases energy. You could attach machines to a bell and make it ring at a tone that is not its resonant frequency, but you would need to put a lot of power into that task. The machines would need to pull and push the edges of the bell at some other frequency and in that task, they would get no help at all from the bell. If you want the bell’s resonant frequency, you have simply to tap it.

While a bell oscillates when struck at a particular volume and then reduces in volume until the “ring” has stopped, electronic oscillators, like the crystal oscillator in a watch, must oscillate continuously for days or decades. Any oscillator requires a resonant element, and a crystal oscillator in a watch keeps its resonant element (the crystal) oscillating by reading the electrical signal from the crystal and then amplifying that signal and applying it back to the crystal with every cycle. It repeatedly “taps” the crystal in order to keep it constantly oscillating.

My watch operates at a fairly high frequency of 32,768 hertz (cycles per second). In an unbelievably accurate clock, like a cesium time standard, the frequency is a very high 9,192,631,770 hertz (abbreviated Hz). WWV, the U.S. national time standard radio station, transmits its precise time markers at 2.5, 5, 10, 15 and 20 MHz (million Hz). While almost any physical thing has a resonant frequency, it must be part of a system designed to express that frequency. The bell doesn't ring without being struck by a clapper, the quartz crystal does not vibrate if it is not stimulated by an oscillator circuit. These systems cause the bell or the crystal to express their resonant frequency by inducing an oscillation: a physical vibration or some other rhythmic change in voltage, water pressure or some other attribute.

I was privileged to participate in a sound healing session which may have been scientific or may have been an hour of airy-fairy new age bunkum. Whether science or bunkum, the sound that resulted in my personal euphoric experience (maybe delusion), was generated by a practitioner rubbing the rim of a quartz bowl with a wooden rod. While I was enjoying the experience, I was also recognizing that quartz is a very unusual material. When it is compressed (whether with a rod or by application of an electrical potential) it generates an electrical potential of its own. Striking quartz causes it to generate a voltage. When that voltage travels through the quartz, the quartz expands. When that expanded quartz returns to its original shape, it generates a voltage which propagates through the quartz and the cycle repeats. This is how a modern timepiece works but it is also why a quartz bowl seems to ring for such a long time and why the sound of a quartz bowl is so unusual.

A quartz bowl, a bowl of gelatin and a brass bell are fairly small resonant elements which, without constant stimulation, will return fairly quickly to a stable state. Something massive like the ocean covers so much area that it is stimulated from innumerable outside forces that no one can fully assess. Watching the ocean we come to understand the amazing forces that drive its dynamism. Over many thousands of square miles between the stimulations of sun and wind and boats and moving creatures within the ocean waters, the ocean is constantly stimulated. The ocean is a connected continuous system. With more sun or less wind, the resonant frequency of the ocean does not change. Oh, the occasional tsunami may question the ocean’s resonant frequency but over the long run, the resonance is stable and visible. With greater stimulation, the wave crests may be higher, but the frequency will remain the same.

As I sat and watched my particular corner of the ocean, I counted about one wave every ten seconds. Is there any possibility that the waves may stop, that the ocean may become a glass-smooth surface of water, that the massive dynamic system of the ocean may quiet? No. It is simply too large for it to stabilize. If any part of the ocean were to become still, the other parts would impinge upon it and it too would again resonate at the local frequency which would, on average, remain fairly close to the overall frequency of the larger body of water.

It was wondrous to see a tiny part of the ocean’s resonance. In my small area, the resonant frequency was a pretty stable 0.1 Hz. Your ocean may vary. Every physical system has a resonant frequency whether made of steel, rubber, plastic or water. When designing a bridge, the engineer takes the resonant frequency of the system into account. The bridge must have a resonant frequency low enough that it cannot be stimulated into resonance by wind, foot traffic or mechanized vehicles. You cannot eliminate a system’s resonant frequency but you can make it different enough from the likely sources of stimulation that it will not amplify that stimulus.

Pay attention to the resonances around you: the swaying trees, the whistle of the wind through a narrow opening, the rhythmic buffeting of the wind in a fast moving car with the windows opened just right. Resonance everywhere will express itself with the right stimulus and will reveal a fundamental and beautiful property of Nature.

Julian S. Taylor is the author of Famine in the Bullpen a book about bringing innovation back to software engineering.
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This work represents the opinion of the author only.

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