Terms Related To Waves | Wave Terminology

Terms Related To Waves | Wave Terminology :- Wave motion can be described quantitatively with the help of certain well-defined terms. These terms related to waves are used to specify various characteristics such as amplitude, wavelength, frequency, time period, phase, and velocity.

• Displacement: Displacement is the instantaneous distance of a particle of the medium from its equilibrium (mean) position at a given time due to the passage of a wave.
• Amplitude: Amplitude is the maximum displacement of a particle of the medium from its mean position during wave motion, and it represents the energy carried by the wave.
• Wavelength (λ): Wavelength is the distance between two nearest points in the same phase of vibration, such as two successive crests or two successive troughs in a transverse wave.
• Time Period (T): Time period is the time taken by a particle of the medium to complete one full oscillation about its mean position.
• Frequency (ν or f): Frequency is the number of complete oscillations made by a particle of the medium per second and is related to the time period by ​.
• Phase: Phase describes the state of vibration of a particle of the medium at a particular instant of time. Particles that are in the same phase have the same displacement from the mean position and move in the same direction at that instant. Phase is a quantity that contains complete information about the vibrational state of a particle in a wave. Mathematically, for a wave represented by the equation y = A sin⁡(ωt−kx), the quantity (ωt−kx) is called the phase of the wave.
• Crest: A crest is the point in a transverse wave where the displacement of the particle is maximum in the positive direction from the mean position.
• Trough: A trough is the point in a transverse wave where the displacement of the particle is maximum in the negative direction from the mean position.
• Compression: In a longitudinal wave, a compression is a region where the particles of the medium are close together, resulting in high pressure and high density.
• Rarefaction: In a longitudinal wave, a rarefaction is a region where the particles of the medium are far apart, resulting in low pressure and low density.
• Wavefront: A wavefront is an imaginary surface that joins all points of a wave which are vibrating in the same phase at a given instant.
• Wave Number (k): Wave number, also called spatial frequency, is defined as the number of wave cycles per unit distance and is given by .
• Wave Velocity (v): Wave velocity is the speed with which the disturbance or wave propagates through the medium and is given by $\lambda$.
• Particle velocity and particle’s acceleration:

  Particle velocity is the velocity with which a particle of the medium oscillates about its mean (equilibrium) position due to the propagation of a wave. It is different from the wave velocity and varies continuously with time. In a plane progressive harmonic wave, the particles of the medium execute simple harmonic motion about their mean positions. Therefore, all the relations of simple harmonic motion are applicable to the motion of these particles. The particle velocity is maximum (±Aω) at the mean position and becomes zero at the extreme positions.

  Particle acceleration is the rate of change of particle velocity with time during wave motion. In a plane progressive harmonic wave, since the particles of the medium execute simple harmonic motion about their mean positions, their acceleration also follows the laws of simple harmonic motion. The particle acceleration is always directed towards the mean position and is proportional to the displacement from it. It is maximum (±Aω²) at the extreme positions and becomes zero at the mean position.