- This article is about waves in the most general scientific sense; a separate article focuses on ocean waves. For other meanings see wave (disambiguation). Soundwave redirects here. For the Transformers character, see Soundwave (Transformers)
The concept wave is related to a disturbance that propagates through space, often transferring energy. While a mechanical wave exists in a medium (which on deformation is capable of producing elastic restoring forces), waves of an electromagnetic radiation, and probably gravitational radiation can travel through vacuum, that is, without a medium in between. Waves travel and transfer energy from one point to another, without any of the particles of the medium being displaced permanently (there is no associated mass transport); instead there are oscillations around fixed positions.
Waves are characterised by crests (highs) and troughs (lows), either perpendicular (in the case of transverse waves) or parallel (in the case of longitudinal waves) to wave motion.
The medium which carries a wave
A medium that can carry a wave is classified by one or more of the following properties:
- A linear medium if the amplitudes of different waves at any particular point in the medium can be added.
- A bounded medium if it is finite in extent, otherwise unbounded.
- A uniform medium if its physical properties are unchanged at different locations in space.
- An isotropic medium if its physical properties are the same in different directions.
Examples of waves
A wave crashing against the shore
Characteristic properties
All waves have common behaviour under a number of standard situations. All waves can experience the following:
- Reflection – the change of direction of waves, due to hitting a reflective surface.
- Refraction – the change of direction of waves due to them entering a new medium.
- Diffraction – the circular spreading of waves that happens when the distance between waves move through an opening of equal distance.
- Interference – the superposition of two waves that come into contact with each other.
- Dispersion – the splitting up of waves by frequency.
- Rectilinear propagation – the movement of waves in straight lines.
Transverse and longitudinal waves
When an object bobs up and down on a ripple in a pond, it experiences an elliptical trajectory because ripples are not simple transverse sinusoidal waves.
Transverse waves are those with vibrations perpendicular to the direction of the propagation of the wave; examples include waves on a string and electromagnetic waves. Longitudinal waves are those with vibrations parallel to the direction of the propagation of the wave; examples include most sound waves.
Ripples on the surface of a pond are actually a combination of transverse and longitudinal waves; therefore, the points on the surface follow elliptical paths.
Polarization
Transverse waves can be polarized. Unpolarized waves can oscillate in any direction in the plane perpendicular to the direction of travel, while polarized waves oscillate in only one direction perpendicular to the line of travel.
Physical description of a wave
Waves can be described using a number of standard 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 crest is the highest point of a wave, while the trough is the lowest point. The wavelength (λ) is the distance between two crests or two troughs that are beside each other. For electromagnetic radiation, it is usually measured in nanometres.
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:
In other words, the frequency and period of a wave are reciprocals of each other.
When waves are expressed mathematically, the angular frequency (ω, radians/second) is often used; it is related to the frequency f by:
.
Travelling waves
Waves that remain in one place are called standing waves - e.g. vibrations on a violin string. 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:
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:
where λ is the wavelength of the wave.
Propagation through strings
The speed of a wave travelling along a string (v) is directly proportional to the square root of the tension (T) over the linear density (ρ):
This equation can be found using dimensional analysis
The wave equation
The wave equation is a differential equation which describes a harmonic wave passing through a medium, discussed above. The equation has different forms depending on how the wave is transmitted, and through what medium.
Not all waves are sinusoidal. One example of a non-sinusoidal wave is a pulse that travels down a rope resting on the ground, extending in direction x, travelling at velocity c. The height of the pulse above the ground is φ. The distance the pulse travels between some time t and time 0 is ct.
In one dimension the wave equation has the form
A general solution, given by d'Alembert is
considered to be the shapes of two pulses travelling down the rope, F in the +x direction, and G in the -x direction. If we substitute for x above, replacing it with directions x, y, z, we then can describe a wave propagating in three dimensions.
A non-linear wave equation can cause mass transport.
The Schrödinger equation describes the wave-like behaviour of particles in quantum mechanics. Solutions of this equation are wave functions which can be used to describe the probability density of a particle. Quantum mechanics also describes particle properties that other waves, such as light and sound, have on the atomic scale and below.
See also
External links
