What affects the energy of a wave
The acceleration amplitude is obtained in the same way
Energy and momentum of a wave
Let the wave function of a harmonic wave be given
The elongation y (t) denotes the momentary deflection of an oscillator of the wave field at the location . The first derivative with respect to time gives the speed of the individual oscillator (not the propagation speed of the wave) at the location at time t to
with the velocity amplitude
and a phase shift of 90 ° between displacement and velocity amplitude.
Energy density - [J / m3] or [N / m2]
For the energy of an oscillator of mass m we get E = Ekin + Epot = Ekin-max:
so you get
Since the energy density is equivalent to a pressure, one also speaks of the radiation pressure pSt..
Points of the same phase position propagate in space with the phase velocity c. If one is interested in the propagation speed of the energy, one arrives at the concept of
Intensity or energy flux density [J / (m2s)]
Current intensity is the amount of energy that moves through a surface element per unit of time:
From this it follows by means of the energy density w:
The size of vSize is generally referred to as group speed - it is the speed with which a certain amount of energy of the wave propagates in space. (If a wave is non-harmonic, it is not monochromatic either. The wave can then be represented as a superposition of harmonic waves, which is called a wave group or wave packet relation
In the case of harmonic waves, the energy will propagate in space with the same speed as the speed amplitude. In our case, the speed amplitude corresponds to the phase position p / 2, which propagates with the speed c. For the intensity we then get:
One can easily convince oneself that because of c = wk the group velocity of a harmonic wave coincides with the phase velocity. Since the instantaneous value of the intensity of a harmonic wave is time-dependent, the intensity is also defined as the mean value of the amount of energy moving through an area cross-section per period, i.e.
Radiation pressure or momentum current density
has the dimension force per unit area. The force itself is nothing more than an impulse current (impulse per unit of time). The radiation pressure is therefore a quantity with the dimension momentum per unit of area and time.
If one wants to determine the force effect of a wave on an area A, then the following applies
with complete absorption of the wave energy (inelastic collision: e.g. absorption of a light wave through a black surface) or
in the case of the elastic reflection of the wave (comparable to the reflection of a ball from a hard wall or the reflection of a light wave from a white surface).
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