"Resonata - a Wave Machine (Java Applet)"


A Wave Machine

The Applet

This is a spring system, designed to demonstrate many of the universal features of waves. Have a play around!

Note: If the applet isn't displaying correctly, or at all, you may need to install the latest version of Java. You could also try the older version of Resonata, which is less demanding of the computer. If you have the latest version of Java and the applet on this page still looks wrong, I'd like to hear about it.

Simplified versions of Resonata for Java-enabled phones are available at oolong.notlong.com, and for Flash here.

You might also like to try out this slightly buggy alpha 3D version (for Windows - let me know if you would like to compile it for other platforms, it should be easy to do).

This is how it works: A series of weights are linked together, so that each is pulled towards its nearest neighbours. This allows waves of motion to travel along the chain. A driving force is applied to one weight, which produces such a wave. Clicking in the display area pulls the nearest weight towards the cursor. When you release the cursor, it twangs back.

Doubling the frequency of the driving force reduces the wavelength by half, since they take half as long to make.
Doubling the wave speed makes the waves twice as long, since they move twice as far in the same time.
The wave speed is controlled by the tension, the strength of the attraction between neighbouring weights;
the speed is proportional to the square root of the tension, so four times the tension means double the wave speed.

When the crest of each wave matches the crest of the next as its returns, resonance occurs.
This happens at the first harmonic, which is also known as the fundamental frequency.
When the ends are looped, this corresponds to a wavelength equal to the length of the chain.
Otherwise the ends reflect the waves, and each one needs to get to the other end and back to meet the next wave,
so the first harmonic has a wavelength equal to twice the length of the chain.
Resonance also occurs at multiples of the fundamental frequency - at only the odd multiples when one end is fixed an the other free, but at every multiple otherwise.

Resonata t-shirts are now available!

This page was developed by Fergus Ray-Murray with the help of funding from Alt-W

Waves in the Real World

The basic building blocks of the universe seem to be either waves or vibrating strings, and most of the things they make up move in bigger waves and vibrations. If we hope to understand much about the physical workings of the universe, then, we need to have some idea about the way that waves and vibrations work. The details of wave motion vary, but many of the principles are universal.

Among the most important concepts to grasp are resonance and standing waves; these are fundamental to countless phenomena in almost every branch of physics. They also underlie the production and perception of speech and music, and have countless applications in engineering. Resonance is what allows gentle pushes to propel a child ever higher on a swing, and it is what allows whipping winds or marching armies to tear asunder seemingly solid bridges.

Broadly speaking, resonance is the reinforcement or creation of an oscillation by an in-coming wave. The energy delivered by the wave will generally be strongest if the wave is at the same frequency as the oscillation, because this allows the two of them to maintain the same phase relationship, so that the direction of the push always matches that of the oscillatory motion. In cases where the vibration is caused by the wave in the first place, the 'natural' frequency is what is important - the frequency at which an object will naturally vibrate if it is excited, as discussed below. If the wave and the oscillation have different frequencies, then sooner or later they will drift out of phase and the motion of one will work against that of the other - however, if the wave is at a multiple of the frequency of the oscillation, a net reinforcement can still result.

The nature of standing waves is closely tied up with resonance, and it is not possible to fully understand one without grasping the other. Standing waves occur whenever a steady wave hits a reflecting barrier; the reflected wave travels at the same speed as the incoming wave, and the peaks and troughs of each interfere with those of the other to make a pattern of 'nodes' and 'anti-nodes' - still points, and points which alternate between being crests and troughs. The strongest standing waves occur when the waves are reflected back again, and fit snugly inside a space which is just the right size and shape to allow incoming waves to be in phase with their own reflections and re-reflections; the frequencies at which this occurs are the resonant frequencies of whatever the waves are in.

This effect, in which reflected waves are bounced back again after a whole number of wavelengths, is one of the most important kinds of resonance, and is the reason why tuning forks, for example, ring at a particular pitch. The fundamental or 'natural' frequency of anything which we ring or pluck to produce tones is generally the main pitch it makes. It amounts to the number of times a sound wave can travel from one end of the object to the other and back again in a second.

It is only waves of this frequency, or multiples thereof (harmonics), which consistently interfere constructively with their reflections and re-reflections. Anything else will soon be out of phase with the incoming wave, so the wave will actually reduce the energy of the system through destructive interference.

Conversely, an incoming sound matching one of the resonant frequencies of an object will cause larger and larger vibrations, limited only by damping - hence the supposed ability of some opera singers to shatter wine glasses, and also the possibility of tuning a guitar by watching the strings carefully.

There are many different types of resonance, and they are important in a wide variety of contexts. Here are a few...

Types of Resonance, and their Applications

Dangers of Resonance

This applet and the accompanying text are currently in active development, and I would be grateful for any feedback on them. Please comment in my forum about them or email me about them, and ask me to let you know about any updates if you are interested.

You could also sign my guestbook.

I would especially welcome feedback from anyone who is learning or teaching about or any related subject - have you found the applet and/or the accompanying text helpful? Did you find any problems with it? Can you suggest any improvements other than what I have listed in my Resonata To-Do List?

Thank you!

See also:

Trigonometry - the underlying mathematics of waves, as well as triangles and circles.

Trochor - an animated virtual harmonograph, one way of visualising harmonies.

Interactive Animation Menu

Main Page

Guest Book

And outside links:

Paul Falstad's excellent physics and maths applets, including several based on waves

Acoustics and vibration animations

Surendranath Reddy's physics applets

'Pythag' and 'Huygens' - two more fun educational wave simulators

Mathematics and Music

GCSE.com waves revision

This page is being developed with the help of funding from Alt-W.

I would also like to thank various members of E2 Science for their helpful feedback.

(site-wide visits since 14/05/2005)