| Revision as of 20:09, 22 October 2001 editDrBob (talk | contribs)3,376 editsm removed "in the case of light"; dispersion also happens in sound waves, etc. | Revision as of 13:39, 3 November 2001 edit undoSodium (talk | contribs)816 edits bigg-ish reorganization +tidy up + more explanation. But still needs more workNext edit → | ||
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| A '''wave''' is a disturbance that propagates. Waves can have a medium which they travel through and can transfer energy from one place to another without any of the particles of the medium being displaced permanently. Instead they ] around a fixed position. | |||
| A '''wave''' is a disturbance that propagates. | |||
| ⚫ | |||
| ⚫ | wave that propagates through air, liquid or solids, and is | ||
| of a frequency detected by the ]; ], observed as ], ], ], etc. In the last case, what propagates is a | |||
| ⚫ | disturbance of the ]. |
||
| '''Examples of waves''' <br> | |||
| ⚫ | |||
| ⚫ | One of the most common waves we encounter is ] - a mechanical | ||
| ⚫ | Also of importance are ] |
||
| ⚫ | wave that propagates through air, liquid or solids, and is | ||
| of a frequency detected by the ]. | |||
| ], ], ]s etc... make up ]. Propagating here is a | |||
| ⚫ | When the perturbation of the particular medium is expressed | ||
| ⚫ | disturbance of the ]. | ||
| ⚫ | in a mathematical way, we obtain some form of the ]. | ||
| ⚫ | For many, the word wave immediately gives a picture of sea-waves, which are perturbations that propagate through water. | ||
| ⚫ | Also of importance are ]s in earthquakes, of which there are the S, P and L kinds. | ||
| All periodic waves are characterized by several numbers: | |||
| '''Characteristic properties''' <br> | |||
| ⚫ | All waves have common behaviour under a number of standard situations. All waves can experience the following: | ||
| The ] (''T'') and ] (''f'') are related by: | |||
| *] - when a wave turns back from the direction it was travelling in due to hitting a reflective material | |||
| :''f'' = 1/''T'' , | |||
| *] - the change of direction of waves due to them entering a new medium | |||
| *] - the spreading out of waves, for exmaple when they travel through a small slit | |||
| *] - the addition of two waves that come in to contact with each other | |||
| where the period is the time taken for one cycle of the wave to repeat itself, and the frequency is the number of cycles per unit time, usually measured in ]. | |||
| *] - the splitting up of a wave depending on frequency | |||
| ⚫ | The ] of a wave is the measure of the magnitude of the maximum disturbance in the medium during one wave cycle, and is measured in units depending on the type of wave. For examples, waves on a string have an amplitude expressed as a distance (meters), sound waves as pressure (pascals) and electromagnetic waves as the amplitude of the ] (volts/meter). The amplitude may be constant (in which case the wave is a ''c.w.'' or ''continuous wave'') or may vary with time and/or position. The form of the variation of amplitude is called the ''envelope'' of the wave. | ||
| '''Transverse and Longtitudinal waves''' <br> | |||
| ⚫ | ] have vibrations perpendicular to the direction of travel, for example electromagnetic waves and waves on a string. ] have vibrations along the direction of the wave, for example sound waves. | ||
| ⚫ | When waves are expressed mathematically, the ''angular frequency'' (ω, radians/second) is often used; it is related to the frequency ''f'' by: | ||
| '''Polarisation''' <br> | |||
| Transverse waves can be ]. This is because transvers waves can oscillate in any angle perpendicular to the direction of travel. Polarisation means to create light which has oscillations in only one line. | |||
| ⚫ | |||
| '''Physical description of a wave''' <br> | |||
| ⚫ | Waves that are moving are called ''travelling waves'', and have a disturbance that varies both with time ''t'' and distance ''z''. This can be expressed mathematically as: | ||
| Waves can be described using a number of variables including frequency, wavelength, amplitude and period. | |||
| ⚫ | The ] of a wave is the measure of the magnitude of the maximum disturbance in the medium during one wave cycle, and is measured in units depending on the type of wave. For examples, waves on a string have an amplitude expressed as a distance (meters), sound waves as pressure (pascals) and electromagnetic waves as the amplitude of the ] (volts/meter). The amplitude may be constant (in which case the wave is a ''c.w.'' or ''continuous wave'') or may vary with time and/or position. The form of the variation of amplitude is called the ''envelope'' of the wave. | ||
| ⚫ | |||
| The period (''T'') is the time for one complete cycle for an oscillation of a wave. The frequency (''F'') is how many periods per unit time (for example one second) and is measured in ]. These are related by: | |||
| ⚫ | where ''A''(''z'',''t'') is the amplitude envelope of the wave, ''k'' is the ''wave number'' and φ is the '']''. The velocity ''v'' of this wave is given by: | ||
| f = 1/T | |||
| ⚫ | |||
| ⚫ | When waves are expressed mathematically, the ''angular frequency'' (ω, radians/second) is often used; it is related to the frequency ''f'' by: | ||
| ⚫ | where λ is the '']'' of the wave. | ||
| ⚫ | f = ω / 2π . | ||
| ⚫ | ] have vibrations perpendicular to the direction of travel, for example electromagnetic waves and waves on a string. ] have vibrations along the direction of the wave, for example sound waves. | ||
| ⚫ | Waves that are moving are called ''travelling waves'', and have a disturbance that varies both with time ''t'' and distance ''z''. This can be expressed mathematically as: | ||
| Transverse waves can be ]. | |||
| ⚫ | ''y'' = ''A''(''z'',''t'') cos( ω''t'' - ''kz'' + φ) , | ||
| '''Properties of wave motions''' | |||
| ⚫ | where ''A''(''z'',''t'') is the amplitude envelope of the wave, ''k'' is the ''wave number'' and φ is the '']''. The velocity ''v'' of this wave is given by: | ||
| ⚫ | All waves have common behaviour under a number of standard situations. All waves can experience the following: | ||
| ⚫ | ''v'' = ω / ''k'' = λ''f'' , | ||
| *] | |||
| *] | |||
| ⚫ | where λ is the '']'' of the wave. | ||
| *] | |||
| *] | |||
| *] | |||
| ---- | |||
| A discussion of the different types of waves would also be appropriate (i.e. in earthquakes there are S, P, and L waves, generalizing to a definition based on a moving pattern or some such). | |||
| Of course, for the above expression(s) to be scrupuluously valid one should add the caveat that exactly the same conditions must apply across all sections of the wave. Hence you could not use it for waves in water coming up a shelving beach... | |||
| ⚫ | When the perturbation of the particular medium is expressed | ||
| ⚫ | in a mathematical way, we obtain some form of the ]. | ||
Revision as of 13:39, 3 November 2001
A wave is a disturbance that propagates. Waves can have a medium which they travel through and can transfer energy from one place to another without any of the particles of the medium being displaced permanently. Instead they oscillate around a fixed position.
Examples of waves
One of the most common waves we encounter is sound - a mechanical
wave that propagates through air, liquid or solids, and is
of a frequency detected by the auditory system.
Light, radio waves, x-rays etc... make up electromagnetic radiation. Propagating here is a
disturbance of the electromagnetic field.
For many, the word wave immediately gives a picture of sea-waves, which are perturbations that propagate through water.
Also of importance are seismic waves in earthquakes, of which there are the S, P and L kinds.
Characteristic properties
All waves have common behaviour under a number of standard situations. All waves can experience the following:
- Reflection - when a wave turns back from the direction it was travelling in due to hitting a reflective material
- Refraction - the change of direction of waves due to them entering a new medium
- Diffraction - the spreading out of waves, for exmaple when they travel through a small slit
- Interference - the addition of two waves that come in to contact with each other
- Dispersion - the splitting up of a wave depending on frequency
Transverse and Longtitudinal waves
Transverse waves have vibrations perpendicular to the direction of travel, for example electromagnetic waves and waves on a string. Longtitudinal waves have vibrations along the direction of the wave, for example sound waves.
Polarisation
Transverse waves can be polarised. This is because transvers waves can oscillate in any angle perpendicular to the direction of travel. Polarisation means to create light which has oscillations in only one line.
Physical description of a wave
Waves can be described using a number of variables including frequency, wavelength, amplitude and period.
The amplitude of a wave is the measure of the magnitude of the maximum disturbance in the medium during one wave cycle, and is measured in units depending on the type of wave. For examples, waves on a string have an amplitude expressed as a distance (meters), sound waves as pressure (pascals) and electromagnetic waves as the amplitude of the electric field (volts/meter). The amplitude may be constant (in which case the wave is a c.w. or continuous wave) or may vary with time and/or position. The form of the variation of amplitude is called the envelope of the wave.
The period (T) is the time for one complete cycle for an oscillation of a wave. The frequency (F) is how many periods per unit time (for example one second) and is measured in hertz. These are related by:
f = 1/T
When waves are expressed mathematically, the angular frequency (ω, radians/second) is often used; it is related to the frequency f by:
f = ω / 2π .
Waves that are moving are called travelling waves, and have a disturbance that varies both with time t and distance z. This can be expressed mathematically as:
y = A(z,t) cos( ωt - kz + φ) ,
where A(z,t) is the amplitude envelope of the wave, k is the wave number and φ is the phase. The velocity v of this wave is given by:
v = ω / k = λf ,
where λ is the wavelength of the wave.
When the perturbation of the particular medium is expressed
in a mathematical way, we obtain some form of the wave equation.
/Talk