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Acoustics Part I: an Introduction to Resonance

Galileo GalileiGalileo discovered the principles of resonance when experimenting with pendulums

Way back in the old days of the 17th century, a man named Galileo Galilei was fiddling around with a pendulum and discovered that if he gave the weight at the end of the string a tiny push at the right time, it would keep swaying back and forth with minimal energy exertion. He discovered that potential and kinetic energy can be set into motion with just a tiny bit of effort. This phenomenon is what became known as resonance. As it turns out, it’s not just pendulums that resonance is affecting. It’s everything. You could say that everything resonates. This affects us musicians and producers in many ways. For example, your room may have too many resonances in the wrong places, which will mess up audio recordings unless you dampen the sound vibrations with sound paneling or bass traps. But since this an intro, I’m sort of getting ahead of myself, and I will cover the practical side of resonance in Part 2.

Nikola Tesla was the archetype of a mad scientist. He invented alternating current, radio broadcasting, and of course, the tesla coil. He is also the subject of many conspiracy theories.

Several centuries later, another guy named Nikola Tesla had heard of this resonance principal, and dedicated his life to discovering how it could be used. Tesla confirmed that everything resonates when he discovered that a pocket-sized mechanical oscillator can cause buildings to crumble and bridges to tremor through the principles of resonance. All that was needed was a pocket-sized piston-driven oscillator sending tuned vibrations into the steel foundations of a building. The power of resonance lies in its ability to multiply force; Just a little bit input energy results in a lot of output energy.

“Although Tesla was not the first to discover resonance he was obsessed with it and created some of the most incredible demonstrations of it ever seen. He studied both mechanical and electrical versions. In the process he created an artificial earthquake, numerous artificial lightning storms, knocked an entire power plant off line in Colorado, and nearly caused the steel frame of a sky scraper under construction in Manhattan to collapse. Tesla realized that the principles of resonance could be used to transmit and receive radio messages well before Marconi.” link

Everything has resonance. Resonance is the principle behind the rattles and vibrations of idle objects caused by the subwoofer hitting a certain note. It is why you can shatter a wine glass with the right audio frequency and a loudspeaker. When the loudspeaker is oscillating at the frequency of the wine glass’ natural resonance frequency, it shatters. Sound waves are pushing the glass at regular intervals, just like you would be pushing the swing, and that regular interval is the same rate that the glass is vibrating. This causes the vibrations in the glass to keep amplifying until the glass can no longer stand the intense shearing action and it breaks into pieces.

This animation demonstrates how air molecules are compressed and decompressed by sound waves.Sound waves propagating through a field of air molecules and reflecting off of square walls

In space, electromagnetic waves are exploding out of stars, propagating infinitely outwards. Once on earth, we can detect these vibrations through our eyes, which are like windows through which a certain band of frequencies can pass through. (Interestingly, our eyes are actually tuned to the atmosphere, because the visible spectrum of light corresponds to the spectrum of frequencies which which pass through the filter of Earth’s atmosphere) We can think of all of our senses simply as vibration sensors that are tuned to different frequency ranges. Our ears sense vibration by directing sound waves towards the ear drums, which are compressed and rarefacted by waves of compressed air molecules. Those little drums in your ears are connected to a bone that wiggles some fluid in the inner ear, which excites even tinier little hairs that send signals to the brain, where that information is finally interpreted into what we know as sound. So, next time somebody asks you “if a tree falls in a forest and nobody is around to hear it, does it make a sound?” you can say that it doesn’t make a sound! It only causes compression waves through the air. If there are no ears to convert compression waves into sound, you could argue that the sound does not exist at that point in time and space.

Figure 1: A graph of a fundamental frequency along with the second harmonic

Each and every system in the universe naturally vibrates at certain frequencies. Theoretically, there is an infinite amount of resonances in any system. Think about it, your body is made of cells, all which have their own resonance frequencies. Your body, which is composed of many smaller sub-systems, has a resonance frequency, just as an organ pipe or a flute or the body of a guitar has a collective resonance frequency. All objects (also known as systems) have a primary, fundamental frequency, as well as many overtone resonance frequencies. The fundamental is the one frequency at which the system sympathetically vibrates the most. The other frequencies at which the system vibrates are comprised of a series of progressively “quieter” overtone frequencies that also vibrate in resonance, but at a lower amplitudes. These are also known as harmonics. Almost all sounds are composed of a series of frequencies all “riding” on top of one another In Figure 1, you can see that when two or more frequencies add up, they produce a new waveform (the resultant waveform in Figure 1). You can produce almost any sort of sound by adding sine waves of different frequencies together (this is the principle behind additive synthesis.

How to find an object’s resonance frequency

“The easiest way to find the resonant frequencies is to place the object next to a speaker and also place a microphone attached to an oscilloscope next to the object. Have the speaker play a tone at a given volume, and then without changing the volume slowly change the pitch (or frequency). If you watch the oscilloscope you will notice that at certain frequencies the amplitude of the wave, which is proportional to the volume of the sound being picked up by the microphone, will be greater than at surrounding frequencies. These are the resonant frequencies, and are detectable as the sound energy absorbed by the object is re-emitted more efficiently at these pitches. Note that you can perform the same procedure, albeit less precisely, in a low-tech way: try holding a large bowl, or coffee can, or some other object that you are hoping to make resonate, in front of your face. Slowly sing a tone with increasing pitch. If there is a resonant frequency in the audible range, you should be able to hear the tone emitted back to your ears at that pitch. Or if you have a piano available to you, try singing into the piano and you’ll see the strings vibrate when you sing their resonant frequencies. ” link

Well, that just about wraps up what I’ve got to say about resonance. In part two of this article, I will explore how resonance principles can help us make informed decisions about recording audio. Do you have anything to say about resonance? Let me know in the comments!

A humorous look at resonance:

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