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Electromagnetic Waves
Published in Myeongkyu Lee, Optics for Materials Scientists, 2019
A wave can be described as a disturbance that travels through a medium from one position to another position. In physics, waves are time-varying oscillations of a physical quantity around fixed locations. Wave motion transfers energy from one point to another. A wave can be transverse or longitudinal. Transverse waves such as electromagnetic waves occur when a disturbance generates oscillations that are perpendicular to the propagation of energy transfer. Longitudinal waves (e.g., sound waves) occur when the oscillations are parallel to the propagation direction. Waves are described by a wave equation that sets out how the disturbance proceeds over time. Consider a transverse pulsed wave traveling in the positive x-direction with a constant speed v, as shown in Figure 1.1. Since the disturbance is a function of both position and time, it can be written as () ψ=f(x,t)⋅
Partial differential equations
Published in Vladimir A. Dobrushkin, Applied Differential Equations with Boundary Value Problems, 2017
Mechanical waves propagate through a material medium (solid, liquid, or gas) at a wave speed which depends on the inertial properties of that medium. There are two basic types of wave motion for mechanical waves: longitudinal waves and transverse waves. In a transverse wave, particles of the medium are displaced in a direction perpendicular to the direction of energy transport. In a longitudinal wave, particles of the medium are displaced in a direction parallel to energy transport. Longitudinal waves are observed, for instance, in elastic bars or rods when their vertical dimensions are small. By placing the x‐axis along the bar’s direction so that its left end coincides with the origin, we can assume that its vibrations are uniform over each cross‐section. Then the longitudinal displacement ux,t $ u\left( {x, t} \right) $ satisfies the one‐dimensional wave equation (11.3.1. In Problems 15 through 20, find longitudinal displacements in rods under the given initial and boundary conditions.
Introduction to Nanosensors
Published in Vinod Kumar Khanna, Nanosensors, 2021
A wave is a periodic disturbance moving in space or in a medium. Waves are of two types: longitudinal (in which the disturbance is in the same direction as that of wave propagation) and transverse (in which the disturbance is perpendicular to the direction of the wave). The wavelength of a wave is the distance between successive compressions and rarefactions of a longitudinal wave (or crests and troughs of a transverse wave). The frequency of a wave is the number of cycles per second, usually expressed in Hertz (Hz). The period is the reciprocal of frequency. Amplitude is the largest difference of the disturbed quantity from its mean value.
Rayleigh-type surface waves in a nonlocal thermoelastic solid half space with voids
Published in Waves in Random and Complex Media, 2021
Lord Rayleigh [30] investigated a type of waves which can travel near the boundary surface of an elastic solid half-space. These waves have wide range of applications in various engineering fields including seismology, acoustics and geophysics. Rayleigh waves are useful for characterization of materials and to find the mechanical and structural properties of the object under examination. Since the existence of Rayleigh surface wave in 1885, this type of surface wave has been studied in different elastic media by a large number of researchers including those listed in this paper. Recently, some significant problems on Rayleigh surface wave propagation in classical thermoelasticity with voids were considered by Bucur et al. [31], Bhagwan et al. and [32] and Bucur [33].
Structural health assessment techniques for in-service timber poles
Published in Structure and Infrastructure Engineering, 2023
Sahan Bandara, Pathmanathan Rajeev, Emad Gad
The stress wave propagation technique is a non-destructive testing method based on the transmission and reflection of a generated stress wave in a structure generated by the application of an external force to the structure. The induced stresses by the applied force transmit to the other points in the body simultaneously with the incident stress wave. Stress waves can be categorised as body waves and surface waves. The body waves consist of compression (longitudinal) and shear (transverse) waves. A longitudinal wave is associated with the propagation of normal stress parallel to the direction of particle motion and a transverse wave is related to the shear stress, where the particle motion is perpendicular to the direction of wave propagation.
Condition assessment tool for timber utility poles using stress wave propagation technique
Published in Nondestructive Testing and Evaluation, 2021
B. Sriskantharajah, E. Gad, S. Bandara, P. Rajeev, I. Flatley
where u is the displacement, x is the position, t is the time and C is the wave velocity. The waves described by this equation can be either longitudinal or transverse (shear) waves. The longitudinal wave velocity (Cl) and shear wave velocity (Cs) can be expressed as follows: