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.noun

a disturbance on the surface of a liquid body, as the sea or a lake, in the form of a moving ridge or swell.

any surging or progressing movement or part resembling a wave of the sea:a wave of the pulse.

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A wave can be thought of as a disturbance or oscillation that travels through space-time, accompanied by a transfer of energy. Wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium —that is, with little or no associated mass transport. They consist, instead, of oscillations or vibrations around almost fixed locations.

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Transverse waves propagate through media with a speed  orthogonally to the direction of energy transfer.

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A transverse wave is a moving wave that consists of oscillations occurring perpendicular (or right angled) to the direction of energy transfer. If a transverse wave is moving in the positive x-direction, its oscillations are in up and down directions that lie in the y–z plane. Light is an example of a transverse wave. For transverse waves in matter, the displacement of the medium is perpendicular to the direction of propagation of the wave. A ripple on a pond and a wave on a string are easily visualized transverse waves.

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Longitudinal waves, sometimes called compression waves, oscillate in the direction of propagation.

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Longitudinal waves have the same direction of vibration as their direction of travel. This means that the movement of the medium is in the same direction as the motion of the wave. Some longitudinal waves are also called compressional waves or compression waves. An easy experiment for observing longitudinal waves involves taking a Slinky and holding both ends. After compressing and releasing one end of the Slinky (while still holding onto the end), a pulse of more concentrated coils will travel to the end of the Slinky.

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a wave refers to how often the particles of the medium vibrate when a wave passes through the medium.

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a wave is the time for a particle on a medium to make one complete vibrational cycle.

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The amplitude of a wave refers to the maximum amount of displacement of a particle on the medium from its rest position. In a sense, the amplitude is the distance from rest to crest.

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The wavelength of a wave is the distance between two corresponding points on back-to-back cycles of a wave. This can be measured between two crests of a wave or two troughs of a wave. The wavelength is usually represented in physics by the Greek letter lambda (λ).

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velocity = frequency * wavelength
or
v = f * λ

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amplitude is A

period is 2π/B

phase shift is C (positive is to the left)

vertical shift is D

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This is the basic unchanged sine formula. A = 1, B = 1, C = 0 and D = 0

So amplitude is 1, period is 2π, there is no phase shift or vertical shift:

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amplitude A = 2

period 2π/B = 2π/4 = π/2

phase shift = −0.5 (or 0.5 to the right)

vertical shift D = 3

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In physics, a standing wave, also known as a stationary wave, is a wave which oscillates in time but whose peak amplitude profile does not move in space. The peak amplitude of the wave oscillations at any point in space is constant with time, and the oscillations at different points throughout the wave are in phase.