Resonance

A long string, under tension from a weight at one end, is mounted horizontally; the other end connected to a variable frequency mechanical oscillator (right). A transverse standing wave can be set up. This is a well-known class demonstration.

As the frequency is increased, at certain frequencies, a series of large amplitude nodes and loops appears. This is an example of resonance. For more detail, look here

The resonant frequencies are determined by the mass per unit length of the oscillator (bass strings have a natural frequency lower than treble strings), also the tension in the string, thus:

Resonance occurs when a driven oscillator is made to vibrate at the same frequency as a driver oscillator. Resonance effects are characterised by vibrations with large amplitude.

This link is from a book

It’s well worth a look or two, if only to illustrate the extent of some of these applications in physics and also the fact that simple harmonic  oscillators are nothing more than periodic exchangers of KE and PE.

Here is a link to  Barton’s Pendulums. You will see this in class. In fact, you might make a set yourselves.

Here’s a video produced by a student

Also – see if you can figure out what’s going on here….

Think about a child being pushed on a swing.

The pusher (driver) pushes at the same frequency as the natural frequency of oscillation of the swing (driven). The result is that the swing oscillates with large amplitude, since the energy it needs to gain amplitude is being supplied at exactly the right time in the cycle. The pusher and the pushed are a quarter of a time period out of phase.

These resonance effects are common. The bus side vibrates as it pulls away, since the metal skin of the bus has the same natural frequency as the engine at low revs. Imperfectly balanced washing machines ‘walk’ across the floor during the spin cycle since the frequency of the vertical component is the same as the natural frequency of vibration of the retaining springs, causing vibrations with large amplitude.  Sometimes , these can be disastrous.  Check out the video of the famous collapsing bridge over Tacoma Narrows in Washington State, called “Galloping Gertie”. Amazing! The bridge collapsed in November 1940 because of a resonant effect between the material in its construction and the wind whistling down the gorge, rather like blowing a reed wind instrument to make a loud sound.

Chladni figures are complex resonant vibrations – or two-dimensional standing waves –  made on a flat sheet and this Irish teacher’s take is very good indeed. Originally, Robert Hooke (yes, him again!) experimented with drawing a violin bow across flour-covered glass plates.

Ernst Chladni  (photo) used the same trick with metal sheets, subsequently with a magnetic oscillator in order to fine-tune the frequencies more accurately. They’re quite fun to watch.

Expensive guitar tables have complex Chladni patterns which account for the characteristics of the instrument.