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Mathematically, the simplest kind of transverse wave is a plane linearly polarized sinusoidal one. "Plane" here means that the direction of propagation is unchanging and the same over the whole medium; "linearly polarized" means that the direction of displacement too is unchanging and the same over the whole medium; and the magnitude of the displacement is a sinusoidal function only of time ...
Spatial position Position of a point in space, not necessarily a point on the wave profile or any line of propagation d, r: m [L] Wave profile displacement Along propagation direction, distance travelled (path length) by one wave from the source point r 0 to any point in space d (for longitudinal or transverse waves) L, d, r
Those waves with the longest wavelengths have phase speeds above v and dissipate into the surrounding water and are not easily observed. Other waves with phase speeds at or below v, however, are amplified through constructive interference and form visible shock waves, stationary in position w.r.t. the boat. Typical duck wake
A plane wave is classified as a transverse wave if the field disturbance at each point is described by a vector perpendicular to the direction of propagation (also the direction of energy transfer); or longitudinal wave if those vectors are aligned with the propagation direction. Mechanical waves include both transverse and longitudinal waves ...
Actually, in general, the wave velocity in a crystal is different for different directions of k. In other words, most crystals are anisotropic for phonon propagation. A wave is longitudinal if the atoms vibrate in the same direction as the wave propagation. In a transverse wave, the atoms vibrate perpendicular to the wave propagation.
r = (x, y, z) is the position vector (in meters). The plane wave is parameterized by the amplitudes. Electromagnetic radiation can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. This diagram shows a plane linearly polarized wave propagating from right to left.
A trough is the opposite of a crest, so the minimum or lowest point of the wave. When the crests and troughs of two sine waves of equal amplitude and frequency intersect or collide, while being in phase with each other, the result is called constructive interference and the magnitudes double (above and below the line).
Particle velocity (denoted v or SVL) is the velocity of a particle (real or imagined) in a medium as it transmits a wave. The SI unit of particle velocity is the metre per second (m/s). In many cases this is a longitudinal wave of pressure as with sound, but it can also be a transverse wave as with the vibration of a taut string.