Everything about Wave totally explained
A
wave is a disturbance that propagates through
space and
time, usually with transference of
energy. While a mechanical wave exists in a
medium (which on deformation is capable of producing elastic restoring forces), waves of
electromagnetic radiation (and probably
gravitational radiation) can travel through
vacuum, that is, without a medium. Waves travel and transfer
energy from one point to another, often with little or no permanent displacement of the particles of the medium (that is, with little or no associated mass transport); instead there are
oscillations around almost fixed positions.
Definitions
Agreeing on a single, all-encompassing definition for the term
wave is
non-trivial. A
vibration can be defined as a
back-and-forth motion around a point m around a reference value. However, defining the necessary and sufficient characteristics that qualify a
phenomenon to be called a wave is, at least, flexible. The term is often understood intuitively as the transport of disturbances in space, not associated with motion of the medium occupying this space as a whole. In a wave, the
energy of a
vibration is moving away from the source in the form of a disturbance within the surrounding medium (Hall, 1980: 8). However, this notion is problematic for a
standing wave (for example, a wave on a string), where
energy is moving in both directions equally, or for electromagnetic / light waves in a
vacuum, where the concept of medium doesn't apply.
For such reasons, wave theory represents a peculiar branch of
physics that's concerned with the properties of wave processes independently from their physical origin (Ostrovsky and Potapov, 1999). The peculiarity lies in the fact that this independence from physical origin is accompanied by a heavy reliance on origin when describing any specific instance of a wave process. For example,
acoustics is distinguished from
optics in that sound waves are related to a mechanical rather than an electromagnetic wave-like transfer / transformation of vibratory
energy. Concepts such as
mass,
momentum,
inertia, or
elasticity, become therefore crucial in describing acoustic (as opposed to optic) wave processes. This difference in origin introduces certain wave characteristics particular to the properties of the medium involved (for example, in the case of air: vortices,
radiation pressure,
shock waves, etc., in the case of solids:
Rayleigh waves,
dispersion, etc., and so on).
Other properties, however, although they're usually described in an origin-specific manner, may be generalized to all waves. For example, based on the mechanical origin of acoustic waves there can be a moving disturbance in space-time if and only if the medium involved is neither infinitely stiff nor infinitely pliable. If all the parts making up a medium were rigidly
bound, then they'd all vibrate as one, with no delay in the transmission of the vibration and therefore no wave motion (or rather infinitely fast wave motion). On the other hand, if all the parts were independent, then there wouldn't be any transmission of the vibration and again, no wave motion (or rather infinitely slow wave motion). Although the above statements are meaningless in the case of waves that don't require a medium, they reveal a characteristic that's relevant to all waves regardless of origin: within a wave, the
phase of a vibration (that is, its position within the vibration cycle) is different for adjacent points in space because the vibration reaches these points at different times.
Similarly, wave processes revealed from the study of wave phenomena with origins different from that of sound waves can be equally significant to the understanding of sound phenomena. A relevant example is Young's principle of interference (Young, 1802, in Hunt, 1978: 132). This principle was first introduced in Young's study of
light and, within some specific contexts (for example,
scattering of sound by sound), is still a researched area in the study of sound.
Characteristics
Periodic waves are characterized by
crests (highs) and
troughs (lows), and may usually be categorized as either longitudinal or transverse.
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.
When an object bobs up and down on a ripple in a pond, it experiences an orbital trajectory because ripples are not simple transverse sinusoidal waves.
Ripples on the surface of a pond are actually a combination of transverse and longitudinal waves; therefore, the points on the surface follow orbital paths.
All waves have common behavior under a number of standard situations. All waves can experience the following:
Polarization
A wave is
polarized if it can only oscillate in one direction. The polarization of a transverse wave describes the direction of oscillation, in the plane perpendicular to the direction of travel. Longitudinal waves such as sound waves don't exhibit polarization, because for these waves the direction of oscillation is along the direction of travel. Although a wave can be polarized by using a polarizing filter.
Examples
Examples of waves include:
Ocean surface waves, which are perturbations that propagate through water.
Radio waves, microwaves, infrared rays, visible light, ultraviolet rays, x-rays, and gamma rays make up electromagnetic radiation. In this case, propagation is possible without a medium, through vacuum. These electromagnetic waves travel at 299,792,458 m/s in a vacuum.
Sound — a mechanical wave that propagates through air, liquid or solids.
waves of traffic (that is, propagation of different densities of motor vehicles, etc.) — these can be modelled as kinematic waves, as first presented by Sir M. J. Lighthill
Seismic waves in earthquakes, of which there are three types, called S, P, and L.
Gravitational waves, which are fluctuations in the curvature of spacetime predicted by general Relativity. These waves are nonlinear, and have yet to be observed empirically.
Inertial waves, which occur in rotating fluids and are restored by the Coriolis effect.
Mathematical description
From a mathematical point of view, the most primitive (or fundamental) wave is harmonic (sinusoidal) wave which is described by the equation where is the amplitude of a wave - a measure of the maximum disturbance in the medium during one wave cycle (the maximum distance from the highest point of the crest to the equilibrium). In the illustration to the right, this is the maximum vertical distance between the baseline and the wave. The units of the amplitude depend on the type of wave — 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 wavelength (denoted as ) is the distance between two sequential crests (or troughs). This generally is measured in meters; it's also commonly measured in nanometers for the optical part of the electromagnetic spectrum.
A wavenumber can be associated with the wavelength by the relation
»
Transmission medium
The medium that carries a wave is called a transmission medium. It can be classified into one or more of the following categories:
A bounded medium if it's finite in extent, otherwise an unbounded medium.
A linear medium if the amplitudes of different waves at any particular point in the medium can be added.
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.Further Information
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