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There are many reasons to count standing waves among waves, the most looming among which are: they are periodic in space in time, which is a common feature of waves (although this is not the case of shock … waves and solitons) they are solutions of wave equations. …

This relation pretty much defines a travelling wave: $$ \mathbf{k}\mathbf{x}-\omega t=const \Rightarrow \mathbf{x}=\mathbf{v}t+\mathbf{x}_0, $$ i.e., the wave front (or the surface pf constant phase) …

Waves can propagate in an inelastic medium, and the fall of dominoes is a wave. … When talking about waves one often means perturbations that are periodic in space and periodic in time at every point. …

Think of every point in space as a harmonic oscillator: specifying its initial position and velocity fully determines its solution (sinc ethe oscillator is described by a second order ODE, a general s …

Sometimes a figure is worth a thousand words:

Group and phase velocities are defined respecively as $$ v_g=\frac{d\omega}{dk}=\left(\frac{dk}{d\omega}\right)^{-1} $$ and $$ v_{ph}=\frac{\omega}{k}. $$ Whether the ration $v_g/v_{ph}$ has a peak de …

Some examples of the waves involving directed displacement of matter are shock waves and solitons. The sea waves close to the shore are another obvious example of such waves. … Waves in water far from the shore in calm weather are a good example. …

If $\psi(x, t) = f(x-vt)$, then $\psi(0,t) = f(-vt)$, whereas $\psi(x,0) = f(x)$. Consequently $\psi(0,t)$ and $\psi(x,0)$ take the same value when $x=-vt$, that is, $$\psi(x, 0) = \psi\left(0, -\frac …

It depends on the boundary conditions and the initial conditions. The situation is a bit more complicated here than in the case of the ordinary differential equations, where the most general solution …

Picture of magnons/spin waves is misleading right? On a more general level, most spin Hamiltonians do not have boson excitations as their solutions. … These appear either as a result of approximations (see, e.g., Holstein-Primakoff transformation), usually implying that only few waves are present or, more formally, as poles in the Green's function (if …

(depending on what kind of waves we are talking about.) … More formally, the frequency of waves can depend on a wave length in a more complex manner, as a function $\omega(\mathbf{k})$ (where I use usual definitions of $\omega=2\pi f$, $k=|\mathbf{k}|=2\pi/\lambda …

Generally, transmitter does not emit in a specific direction - e.g., a radio station would emit signals in all directions (as a spherical or cylindrical wave), so that whoever has a receiver can recei …

What you are doing is a very simple model, where a drop is considered a point-like (1) and instantaneous (2) perturbation, and the resulting waves are treated as two-dimensional surface waves (3) (although … there may be also waves going into the depth). …

What is really meant in question is Bohr model of atom rather than the de Broglie hypothesis that particles are waves that can be assigned frequency and wave vector in terms of their momentum and energy … Bohr model simply postulates selection rules, that is the transitions occur only between the states that correspond to standing waves. …

Field (physics): In physics, a field is a physical quantity, represented by a scalar, vector, or tensor, that has a value for each point in space and time. So yes, indeed, (continuous) distributions …