Waves+and+Oscillations

What are waves?
When waves are mentioned most of us will think of waves at sea, or crashing into a beach. However waves are all around us all the time. For example, sound waves allow us to hear, while electromagnetic waves allow us to see; microwaves are used by mobile phones, while radio waves are used to broadcast news and entertainment across the country.

Waves can also cause problems for engineers in objects that we tend to think of as pretty solid. For example, earthquakes can cause waves which shake the ground and buildings, while in 1940, winds caused vibrations in the Tacoma Narrows suspension bridge which caused it the collapse of the bridge (although as explained in a number of places, including minutephysics ([|Tacoma - the real reason]), this was not due directly to resonance, but due to aeroelastic flutter, however the 'bridge' waves in the video below are still a dramatic example of a torsional (twisting) wave.

The video on the right shows the collapse of the Tacoma bridge (although you might want to turn off sound before watching... unless you are a fan of Evanescence...) media type="youtube" key="mniN0L0Gq_0" height="315" width="420" align="right"

The examples of waves above cover four different types of waves:
 * Longitudinal waves (e.g. sound waves and certain waves in solids (including p-waves from an earthquake))
 * Transverse waves (e.g. waves at sea and certain waves in solids (e.g. s-waves from an earthquake))
 * Electromagnetic waves (e.g. light, microwaves and radio waves)
 * Torsional (twisting) waves (e.g. in Tacoma bridge)

The first two of these types of waves are considered below, as well as their common defining characteristics (e.g. speed, frequency, wavelength and amplitude). Electromagnetic waves are transverse waves, however they differ from most the transverse waves that are familiar to us (e.g. water waves) as they are not //mechanical waves//. Mechanical waves are waves (transverse or longitudinal) that involve oscillations //of the medium// through which the wave travels. Electromagnetic waves do not require a medium to travel as they are made up of oscillations electric and magnetic fields, and hence can propagate through a vacuum. Electromagnetic waves and other specific wave related topics can be found by following the links below.
 * Electromagnetic Waves
 * Simple Harmonic Motion

Describing waves
To describe a wave, a number of terms need to be defined:


 * ~ Term/symbol ||~ Definition/description ||
 * Displacement || This is the distance that a point on the wave has moved away from its equilibrium position at any moment in time. (NB the equilibrium position is where the point would be in the absence of a wave - think of a lake which is completely calm, and flat, or at rest. If you drop a pebble in then the surface will be displaced either up and down from that rest position by the resulting wave. ||
 * Amplitude || This is the maximum displacement caused by the wave of any point away from its equilibrium position. ||
 * Wavelength/l || This can be thought of a number of (interchangeable) ways: (i) the distance between two successive peaks of the wave (or two successive troughs), or more generally (ii) the distance between two successive points on the wave that are in phase (where points are "in phase" if they have the same displacement and direction of movement), or (iii) one complete cycle of the waveform. ||
 * Time Period/T || The time taken for a complete cycle of the wave to pass a point. ||
 * Frequency/f || The number of complete waves that pass a point in a second. ||
 * Speed/c || The speed with which the wave travels (NOTE: for a mechanical wave this is NOT the same as the speed the medium is moving). More generally this could be defined as the speed with which energy is transferred by the wave. ||
 * Phase difference || If you can generate two identical waves, but you start generating one wave just before the other, then you will have two identical waveforms, but the peaks of one will arrive at a point slightly before the other. The waves are said to be out of phase. ||

These terms are also shown pictorially on the right.

Note, that to show wavelength on a graph, the x-axis must be distance from source (as opposed to time, where the peak-to-peak distance is then the time period of the wave).

Furthermore, it may be seen from the definition of time period (or just period) that it is related to frequency as follows:

(1) T = 1/f

Finally, the relationship between the speed, frequency and wavelength of a wave can be derived from the definition of speed = distance over time. As the distance travelled by the wave in one time period is equal to l, we can write:

(2) c = l /T

And substituting (1) above:

(2) c = fl

Although the diagrams of the waves on the right might be assumed to refer to transverse waves, that will actually depend on what 'displacement' the y-axis is referring too. For a longitudinal wave, the displacement will be parallel to the direction the wave travels, while for a transverse wave, the displacement will be perpendicular to the direction the wave travels (see below)

Longitudinal waves
In general, a longitudinal wave can be defined as follows: The most common example of a longitudinal wave is a sound wave. Sound waves are created by something moving the medium (frequently air) through which the sound will travel, for example, by plucking a guitar string, or by the vibrations of your vocal cords. The waves longitudinal waves created by a guitar string are shown in the picture on the left, below. (Note that the way a guitar generates an audible sound wave is more complex than this, involving resonance in the sound box, but this is ignored for simplicity.
 * //A longitudinal wave is a wave where the direction of movement of the medium is parallel to the direction of the wave. Or, where the displacement of the particles is parallel to the direction of propagation of the energy of the wave.// ||

The movement of the guitar string outwards (to the right, in the picture) pushes the nearby air, creating an area of higher pressure (a compression). As the air molecules in this compression move around, colliding with other molecules, they transfer their energy to nearby molecules. In this way the compression moves through the air quickly, even though individual molecules are not moving very far. In addition, the movement of the string away again creates an area of low pressure (called a rarefaction) which follows the compression out to form the sound wave.

As with all mechanical (i.e. physical) waves, it is important to recognise that any single point in the medium itself is only oscillating about an equilibrium (rest) position, and does not move along with the wave. The wave transfers energy through the medium, but the medium itself stays where it is (on average).

Other examples of longitudinal waves are waves sent along a stretched spring by a movement of one end of the spring in the direction of the spring, and p-waves in an earthquake.

The animation above, right, represents a longitudinal pulse moving through a medium. (A pulse is just a single wave (a compression and rarefaction) moving through a medium by itself).

//Sound Waves - lesson idea//
Out into playground to measure time for echo from gym wall - to estimate the speed of sound.

Transverse waves
__Ripple Tank Applet__

The above is a really useful demo of wave motion that can be used as a sandbox for experimenting: [|Ripple Tank Applet]. Note that the settings allow you to set the wave up as a sound wave or light wave. If should be noted however that if thinking of them as sound waves, then (as sound waves are longitudinal waves) the wave-fronts represent the areas of compression and the spaces areas of rarefaction, rather than the peaks and troughs of water (longitudinal) waves. In addition, the sound waves are correctly shown in the ripple tank applet as being reflected without a phase change (as a compression arriving at a fixed boundary would be reflected as a compression), so the "acoustic waves" option should be turned OFF when using the ripple tank applet to demonstrate what would happen in an actual ripple tank.

__Ripple Tank Videos__

In addition, here are some videos of various ripple tank experiments, using the sort of kit that a school should have easily available. These videos are best viewed in Quicktime (or any other player that allows the "slider" to be used to play the video manually, so you can find the speed that gives the clearest results). I would also advise that you turn the sound off! You can follow the link to a webpage on which they are all uploaded, or follow the separate links to download the files to your own computer.

Link to webpage with quicktime videos

[|Ripple tank - straight waves] [|Ripple tank - straight waves relected against and angled barrier] [|Ripple tank - straight waves reflected in a concave barrier] [|Ripple tank - straight waves reflected against a convex barrier] [|Ripple tank - straight waves into shallower water] [|Ripple tank - straight waves through medium gap in barrier] [|Ripple tank - straight waves through narrow gap in barrier] [|Ripple tank - straight waves over shallow lens]