Everything Resonates
Hold down the rightmost pedal on a piano and shout into it loudly. “Aah!” Surprisingly, the piano replies with a soft echo, “aaaa.” But how can the piano make a sound if nobody has touched the keys? Welcome to the beautiful world of resonance, one of the most seemingly magical phenomena in all of science.
From a few differential equations describing vibrating systems emerges the wonderful and unique property of resonance. It can cause buildings to fall apart, and wine glasses to shatter from mere sound. At the same time, it is resonance that gives music its sonority, impact, and raw emotional power.
The science behind resonance is surprisingly simple. Many mechanical systems settle in an equilibrium, like a straight string on a guitar. But under a little perturbation, such as a pluck, the system will “oscillate” or vibrate about equilibrium. The particular way it vibrates depends on the details of the system. For example, the low E string on a guitar vibrates more slowly than the higher A string, because it is thicker. The number of times a system tends to go back and forth in a second is a special characteristic that scientists call its “natural frequencies.”
It turns out a system can begin vibrating all “by itself,” without explicitly “being plucked!” This happens when some other source happens to have a frequency near a natural frequency. For example, someone else playing the same pitch nearby can cause the low E string on a guitar to start vibrating, just on its own, even if the guitarist doesn’t pluck the string. More surprisingly, this only happens if the pitch, or frequency, is similar – if it is too different, the system barely responds. This seeming magic is really the beautiful result of equations describing the system’s dynamics.
This begs the question of why a piano seems to sing when a crazy musician shouts at it. Well, a piano has over 200 strings at many different pitches, some of which happen to “like” the shout, or have natural frequencies near the shouts’ frequencies. Those strings get “excited” and start vibrating, and the piano’s soundboard amplifies the vibrations, giving off the sound of the “slight echo” that stays after the shout.
But resonance’s scope is much broader. Anything that vibrates can resonate – and quite literally everything in our world vibrates because things are in some kind of equilibrium. Take a wineglass. We can “pluck” wineglasses by tapping them with spoons, and they give off a sweet ”ding” as they vibrate and dance around. But this means that any other sound of the same pitch can cause the wineglass to start ringing and resonating. If this sound wave is loud enough, it transfers so much energy into the wineglass that it vibrates too much and shatters. Some folk stories even tell of opera singers so powerful they can shatter wineglasses with their voices alone. Sadly, at a reasonable distance of a few meters, the unamplified human voice can’t quite produce the intensity of sound needed. But with a much larger sound intensity, say, a trumpet blasting fortississimo right into the edge of a wineglass, is such a feat possible? Perhaps.
Another fun, easy way to experience resonance is with 2 identical empty milk jugs. Ask someone to blow across the top of a milk jug to make it sing like a flute, and hold up another one to your ear. The jug doesn’t shatter the way a wineglass does, but it does whisper, because the other milk jug’s sound excites the air inside it to oscillate. This style of resonance is what helps give music its power – imagine that sound came from flutes instead of jugs. Here, the acoustic response is much greater, because their instruments are designed to be sympathetically resonant. When musicians play together in tune, the resulting sound is “greater” than the sum of its parts because the musicians physically support the sound coming out of each other’s instruments. This is one reason why live orchestra performances are so incredibly powerful.
Resonance not only breathes life into music, it also has plenty of practical applications. It allows us to tune radios, for instance. These inventions rely on the fact that systems only respond to frequencies that are near their natural frequencies. We don’t hear all radio stations playing at once, but only a single one, because electrical circuits in the radio are tuned to only respond to a narrow bandwidth.
Buildings can also resonate – but in this case the vibrations aren’t sonorous or desirable. When some outside driving force such as an earthquake comes in at just the right frequency, the resulting vibrations can damage skyscrapers and dizzy their rich upper-story tenants. As such, when engineers design buildings, they need to consider how it vibrates and take safety guards to dampen the oscillations.
One of the most interesting ways they accomplish this is with a “tuned mass damper,” famously found in the Taipei 101. The damper is designed to have the same natural frequency as the building, so that when the building vibrates, the damper is excited and starts moving back and forth. However, the damper is damped, meaning that it dissipates the energy that the building transfers to it. Essentially, it acts like a shock absorber, but it also uses principles of resonance to be far more effective by specifically only absorbing vibrations of the building’s particular frequency. This elegant piece of engineering is a testament to the power of science. Not only can we predict that our buildings can be damaged by certain earthquake waves, we can also cleverly design a way to protect them and save countless lives.
Next time you are at a live music performance, consider all the astounding science that goes on inside instruments and all around that enhances the experience, and appreciate the beautiful phenomenon of resonance that science has enabled us to understand. The principles of resonance are everywhere in our everyday lives – you just have to look for it.
Works Cited
Feynman, Richard P., Robert B. Leighton, and Matthew L. Sands. The Feynman Lectures on Physics. Vol. 1. Reading: Addison-Wesley Pub., 1963. Print.
Hillhouse, Grady. “Tuned Mass Dampers in Skyscrapers.” Practical Engineering, http://practical.engineering/blog/2016/2/14/tuned-mass-dampers-in-skyscrapers. 04 Nov. 2016.
