Swing

Rock, swing, pop and all that jazz! I won’t blame you if you thought this is all about music and dance. What I’ll be talking about is something called resonance. This has to do with how certain things vibrate. Music may be defined as a neat and pleasant arrangement of harmonious sounds. And sound comes from things vibrating. Whether it’s the plucked strings on a rock guitar or the undulating drum skins or the air trapped in a tuba, music is all about vibrations. There is a whole topic in physics which deals with this natural phenomenon called vibration. We sometimes interchange the term ‘vibration’ for ‘wave’ and, to be fair, it is fine to do so. So, first things first. What is a wave? And what has this got to do with swings and rocks?

Swing

A wave is a disturbance. To think that the soothing notes from a piece of spa music actually originates from a disturbance can be… disturbing. But this is where sound waves come from: a source of disturbance.  What is being disturbed, is the next logical question. A medium. Not the sort who channels spirits from worlds beyond our own but the sort that acts like a carrier. What does it carry? Energy. What kind of energy? Well that depends on the source emanating that energy. It can be energy in the form of light whereby the source is some light bulb in a room. It can be energy in the form of sound whereby the source is a piano. Sound energy can only propagate in a material medium. By this, we mean that it can travel through gases, liquids or solids. It cannot travel through a vacuum. In contrast, light energy can travel through a vacuum. This is because the medium that it can travel through is immaterial. It travels through a medium we call a field. And the name we give to this field is the electromagnetic field. Disturbances in that field are the sources of the light energy. The disturbances then propagates through that field.

A good analogy of this is water waves. Imagine a placid pond. The water in that pond is initially undisturbed, it’s completely levelled and is as flat as a sheet of glass. Next, plunk a stone in the middle of the pond and observe how that disturbs the surface of the water. It causes ripples to form at the point where the stone plunged into the pond. Those ripples, in concentric patterns, propagate outwards from their origin and travel along the water surface towards the perimeter of the pond. Those waves are essentially a disturbance in the water. The medium they travel in is the water. And they carry a portion of the kinetic energy of the sinking stone. All of this is a very familiar scene. We’ve all witnessed the ebbs and flows of water waves or the ripples in puddles or the terrifying tsunamis. Waves are ubiquitous.

To carry on with that placid pond analogy, once those waves have propagated over the whole pond and rippled back and forth from the edges of the pond to its source, the waves will gradually subside and die out. The pond will eventually regain its composure and tranquility and be flat again. If you want to see the waves again, there needs to be another disturbance in the water. To keep the wave going on and on, that disturbance should be continuous. So this will be equivalent to throwing stones into the pond one after the other, in a timely manner. As long as you have enough stones with you and as long as you keep throwing them in the pond, the waves will keep forming and rippling. This idea of a continuous disturbance and wave formation is closely linked to another phenomenon in physics called oscillation. Oscillations come in various forms and exist in different media. Perhaps the most common form of oscillation is the pendulum.

The swinging pendulum is a classic example of how a moving object oscillates from one position to another. Typically, pendulums oscillate from side to side. But you can have oscillatory motion in the up and down direction as well. Think of an object tied to a spring and left to hang freely. By pulling downwards on the object and letting go, the object bobs up and down as the spring contracts and expands. This is also an example of an oscillatory motion. Just like the pendulum going sideways and the spring going up and down, you can have other types of oscillations which go in both directions at the same time. When light energy propagates as a wave, it oscillates both ‘sideways’ and ‘up-and-down’. Well, the reason I’ve put those two terms in quotes is because the oscillation is not strictly always on the horizontal and vertical. They can be in any two directions as long as these directions are perpendicular to each other. In any case, the point is that, this kind of a wave oscillates in two (perpendicular) directions at the same time. Sound waves, on the other hand, will oscillate in one direction only. It will do so either sideways or back and forth as it moves along the direction of propagation.

Whatever the type of oscillation, there is one thing that they all have in common. Their motion involves something called frequency. What frequency tells us is how many oscillations took place with each ticking second. The more oscillations there are per second, the higher the frequency. Let’s go back to our example of the pendulum. Suppose we have a pendulum that is happily at rest in its vertical position. No disturbance at all, for now. We take hold of the bob, pull it sideways and stop there. From where it was to where it is now, there is a given horizontal distance. It’s been displaced by a given amount. This amount is what we call the amplitude. From that position of maximum displacement, therefore, we let go of the bob. It swings right to the opposite side, stops, and swings back to where it came from. Upon returning to its initial position of maximum displacement, it completes 1 oscillation. But it doesn’t stop there. It swings from side to side. Each time it returns to its initial position, it completes yet another oscillation. We count the number of oscillations it does in 1 second. This is what gives us the frequency of the swinging pendulum. Waves also have this property called frequency and it is also about the same thing: the number of oscillations completed per second. So, what is special about this property called frequency?

A priori, it is just another physical quantity that we can measure. Nothing fancy there. However, what is interesting is this following little fact: every single thing in the universe has a this very peculiar property called the natural frequency. And this is where things start to get more exciting. A swinging pendulum stops being such a dull and hypnotising experiment when natural frequency kicks in. If a system is made to oscillate at its natural frequency, its amplitude increases with every oscillation. In effect, the oscillations become more and more significant. Imagine pushing someone on a swing. That someone-on-a-swing system has a natural frequency. If the person pushing the swing matches the natural frequency then the swing will oscillate, or go back and forth, with greater and greater amplitude. That is, the swing will be able to reach higher and higher as long as the person pushing the swing does so at the natural frequency. What is happening in that instance is that, the swing system is accumulating more and more energy with every oscillation. The energy comes in the form of kinetic energy, or energy of motion, from the person pushing the swing. That person is in effect ‘feeding’ energy into that swing system with every push. This accumulation of energy is displayed in the form of increased amplitude of oscillation in the swing.

There is another familiar system which displays such behaviour of increased amplitude of oscillation when made to vibrate at their natural frequency. The microwave oven is based on this fundamental principle. Water molecules jiggle around in water. Every liquid, in fact, is composed of tiny molecules vibrating  and jiggling about. As a result of their moving about, they possess kinetic energy. If we sum up all the kinetic energies of the molecules, we come up with an amount of energy which we interpret as the temperature of the liquid. In essence, the greater that energy, the hotter the liquid. If that energy reaches a certain point, then the liquids starts to change into a gas. Thus, boiling occurs. Now, how can we make those molecules move faster and with greater amplitude? We have to shake them about or push them (just a we push a swing) at their natural frequency. We do so by sending electromagnetic signals at that particular frequency. Those signals become the drivers which push those water molecules at their natural frequency. As a result of all this, the water molecules move with higher amplitude and more speed, the faster they move, the more energy they have and all this adds up to is an increased in temperature in the liquid. Since most food product contain water, then we can heat them up in a microwave oven because of this.

This phenomenon, whereby systems oscillate with increasing energy when subject to vibrate at their natural frequency, is known as resonance. Hence, another name for natural frequency is resonant frequency. Resonance can be a good thing. When it is about heating up one’s dinner then we are all for resonance. But, it has its bad side as well. When glass is made to vibrate at its resonant frequency, it eventually cracks and goes pop. It is known that some people can shatter glass just with their voices. By singing a constant note of a given pitch or frequency, they are able to ‘lock in’ to the natural frequency of some sheet of glass and cause it to vibrate more and more until it cracks. Cracks, not just on glass but also on other materials such as rock, can occur because of resonance. When those cracks are found in buildings or bridges then, of course, this is a bad thing.  When tuning a radio or TV, then we are in  effect locking on to the resonant frequency of the tuner to the signals being transmitted. When undergoing an MRI scan at the hospital, we are in effect subjecting the nuclei of the atoms in our body to resonate at a given frequency so that these changes in the magnetic field can be picked up by the scanner and an image of the inside of our body formed for medical examination. MRI is short for Magnetic Resonance Imaging. It is about creating an image of the inside of our body using powerful magnets that cause the nuclei of the atoms in our body to vibrate at a resonant frequency.

Resonance, therefore, can have either desired or disastrous consequences. Resonance can occur in different kinds of systems. From mechanical ones, like swings, to audible ones to magnetic ones and even gravitational ones. Some planets and their moons are ‘locked in’ some gravitational push-and-pull among each other. Those gravitational tidal forces eventually settle in some resonant frequency. What that means is that those moons revolve around their planet at given periods. If, for example, the first and closest moon, takes 1 month to go round the planet, then the second moon could take 2 months and the third and furthest would take 4 months. Their period of revolution, which is none other than the inverse of the frequency of revolution, is therefore bound in that cycle. This is when they are in resonance. Sometimes these orbits are stable. There can be cases when gravitational resonance become unstable and the system then collapses.

As you can see, this very simple natural phenomenon we call resonance has reaches far beyond the mundane systems of swings and rocking chairs. They span all kinds of systems, from material to non-material ones, from liquid to astronomical ones, for good or bad consequences. Resonance is yet another example of how physics is not an isolated, textbook-based subject, weighed down by equations and mired by obscure laws and principles. On the contrary, it explains how things behave and it finds patterns and similarities in seemingly different systems. It reveals their true nature and sheds light on what other possibilities might exist in our vastly wonderful universe.

So, whether it is about sound, music and all that jazz or whether it is about orbiting moons, remember that physics is the key to explaining the natural world. That is, for me, a reassuring thought.

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