How vibrations travel
Physics Narrative for 14-16
Periodic variations that travel: do like me, but later
Do like me, but later, is the fundamental instruction that allows influence to propagate from source to detector. People don't much like spooky action-at-a-distance, so you might reasonably ask how this instruction really happens. Then you'd have a more convincing story.
You know the instruction can arrive, bringing a signal with it if that was encoded before the signal left the source – more on that later on in this episode. For now, every time you turn on a radio, or, more simply, listen to recorded music from a loudspeaker, you verify this functionality.
You'll also know that such an influence can cause an energy store to be depleted, associated with changes at the source, and another to be filled, associated with changes at the detector. Feel the Sun on your cheek on a summer's day or float amongst the waves just off a beach, and you'll be able to think of the stores being emptied and filled by a kind of remote working. The physical changes leading to the local store being filled are close, but the physical changes resulting in the distant store being filled may be a significant distance away – from metres, through hundreds of kilometres, to 8 light-minutes away in these examples.
This is all very abstract – and therefore of wide applicability, as it describes all kinds of radiating – without reference to the physical basis of whatever is vibrating.
Yet sometimes we'd suggest its worth knowing about the mechanisms, even if this adds complexity, as such detail makes links to other bits and pieces of knowledge and helps show how they are all connected together. Seeing these interconnections is part of doing physics, and often the most creative and fruitful part, as such connections often help to illuminate new topics.
So, what's doing the vibrating – that is, what is the source setting into repetitive motion, where it is sensible to be able to say that it has both a frequency and an amplitude? Let's start with light and with sound. These are very different – physically different. One needs tangible particles to vibrate; the other needs only an electromagnetic field. Some of the properties of these two kinds of vibrations were elucidated in the SPT: Sound and SPT: Light topics. These two can serve as prototypes: sound for mechanical vibrations; light for the whole electromagnetic spectrum.
We'll deal with the mechanical first, but we'll still need to think about two different situations – fluids and solids. In these two the forces between the particles are rather different, so setting some particles moving and then seeing how that movement is imparted to adjacent particles might be expected to be different.
Linked masses and springs: modelling the essentials of things that vibrate
Choose a blade of grass, or a branch, and deflect it. It waggles to and fro, or vibrates, a few times before coming to rest. For it to vibrate like this there must be a force that restores the object to its resting location, starting the repetitive movement with an acceleration as it is released: this force is provided by the branch or blade. But when it reaches the resting location it overshoots, continuing past its undisturbed location. So there must also be some mass, so that, once moving, it keeps moving – this is again provided by the blade or branch.
There are two effects here, both apparently as a result of a single object. To build a simple model, we suggest assigning each effect to a separate element within the model: these will be provided by a spring and a mass. So we re-imagine the blade or branch as a mass between springs. You could get away with a single spring, but many people find it easier to appreciate the symmetry of the situation with a more symmetrical (although still one-dimensional) model.
This system of a mass-between-springs is our prototype vibrator or oscillator. Many, many systems can be modelled using this as a basis, on all kinds of scales (from absorption of particular frequencies by ammonia clouds in deep space, through human locomotion, to the response of buildings to earthquakes, and well beyond), but our concern here is to show how it can form the physical basis for one kind of wave. One such mass-between-springs system must be connected to another, so that what one does, another does later:
do like me, but later is the key to a propagating radiation. Then we'll have the
how of one kind of travelling vibration.
All that is necessary is to link one vibrator to another, so that the deflection of one causes a deflection in the other. So when one deflects, it exerts a force on another. This sounds just like a job for a spring (again – why invent a new idea when you can reuse an old one with which you are familiar?): a change in distance between two things connected by a spring results in a force exerted by one on another. So add extra springs linking the two. And because the second vibrator in the chain takes time to accumulate a velocity and time to accumulate a displacement, there is automatically a delay built in. There's more detail on this in the SPT: Force and motion topic.
This now looks remarkably like the mass and spring model used in the SPT: Forces topic to explain warp forces. It's not surprising that solids can support radiations – or sounds, as we'd normally call them. These are longitudinal vibrations, as we've drawn here, resulting in density variations propagating through the solid. Sounds are travelling, or propagating, periodic variations in density.
There is nothing to prevent solids from supporting travelling transverse vibrations as the springs still provide a restoring force if we pluck an individual mass, so displacing it vertically. Exactly the same is true if we generalise to two and three dimensional lattices of masses and springs.
Plotting out propagating changes
You can plot the variations in density over time, or take a snapshot of the propagating changes. That is what we have done here, choosing to plot a variety of things. You can see a time trace being plotted out in the SPT: Light topic.
Now start with a completely different situation – a pair of charged balloons – as a model of two charged particles a long way apart. These are initially in equilibrium, so there are other electrical forces acting on the balloons. Again, there is a force between the balloons, so that moving one exerts a force of a different value on the other. (More on the electric force in the SPT: Forces topic).
There are always lots of electrical forces around as matter is electrical, so here we'll concentrate just on how the changes in the location of one balloon affect the forces on the second.
The force between the pair is radial, joining the centres. Now move the first ballon (the source) up and down, as if it is vibrating. What difference does this vibrating have on the detector (the second balloon)?
The effect on the second balloon will be that the electrical force points in a new direction. While this change is happening, there is a kink that travels outwards, as the information about the change in direction of the force moves out from the source. (The electric field was in one direction: now it's in a different direction. The kink is the change in the field.) This kink gets sharper the further you get from the source, as the radial component gets smaller and smaller. (Do you remember that the electrical force decreases as you get further from the charge?) So the kink becomes closer and closer to being at right angles to the line joining the balloons. The propagating change is at right angles to the original force. Waggling a charge up and down sends out a whole series of such kinks, and results in a series of transverse vibrations in the electric field that propagate outwards from the source, affecting charged particles as they go. This is an electric wave.
Linked changes: electromagnetic waves, electric forces and magnetic forces
Electrical changes are always linked to magnetic changes – just how was explained in the SPT: Energy and electricity topic. So a spreading electrical kink in the lines of electrical force – and so electrical waves, will always be linked to a spreading magnetic kink in the lines of magnetic force – magnetic waves. These kinks spread at the speed of light: they are electromagnetic radiations. These radiations can have many different frequencies, set by the source, as ever, but they are all members of the same family, because they all travel or propagate with the same mechanism.
The working you are doing in waggling one charge here shifts energy as another charge waggles a long way off. Does this sound familiar? It should do: in electric circuits, the charged particles in the bulb are worked on at a distance by the battery. The electromagnetic wave is a development of the treatment of alternating circuits.
There is another intriguing facet here: the electric vibrations must be at right angles to the direction of propagation, but that still leaves many different planes available for the vibrations – the full 360 degree. This leads to an account of the phenomenon of polarisation, in episode 03.
Fluids: describing the vibrations as variations in density
Now for fluids. Take a bicycle pump. Put one finger over the end and push in the plunger. You have deflected the plunger just as you deflected the blade of grass. Release the plunger and it will spring back driven by
the spring of the air. As it does so, so there is a rush of air particles, thus a moving mass. The pump will
damp down any oscillations, but if there were no friction you could imagine that the rush of air particles would not stop at the resting location but move through that until pulled back by the accumulated effect of the force acting on these particles (another
spring of the air – but this time more like a spring under compression rather than under tension).
So gases, and also liquids, can vibrate, and these vibrations can be moved from one region of the fluid to another. The displacement of the particles in the fluid from their resting position results in a change in density – more particles are packed into a smaller volume. This increased density leads to an increase in pressure. This variation in pressure from the normal provides a restoring force (see the SPT: Machines topic for more on the relationship between the pressure in a fluid and the forces acting on surfaces surrounding that fluid). This restoring force then causes the accelerated particles to overrun, resulting in a lower than average density, and so lower than average pressure. This variation in pressure from the normal results in another restoring force, still directed towards the resting position.
This rushing to and fro affects the surrounding particles, and so the vibration is communicated to the neighbours. A simple presentation of the end results can be found in the SPT: Sound topic.
However, because of the mechanism outlined here, fluids can only support push–pull, or longitudinal, waves. The variations in density only cause restoring forces in the direction of propagation of the radiation: the movement of particles and propagation is all in one plane.