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In a classical view of the physics, the energy of a wave depends on the emitting energy of the wave surface, independently from the kind of wave.

Thus the question has not a clear answer: more energy the source emits, higher the wave energy independently from its type.

The situation completely changes in quantum mechanics, where waves and particles are related, being aspects of the same phenomenon.

Not only quantum fields, like the electromagnetic field and the Dirac field (the quantum field associated to electrons) are associated to particles populations, but also field coming from collective motion of macroscopic objects (as the waves on the surface of water or elastic waves in a solid) can be associated to the so called pseudo-particles (those associated with elastic waves are called phonons).

In this more complex view I can interpret the question as what wave is associated with the most energetic particle, since the averagewave energy is nothing else that the energy associated to a particle multiplied by the average particle number.

Since the special relativity link energy to mass with the equation

E=m c^2

more massive and faster are the particles, more energy is related to a single particle.

For example a single relativistic electron (at a speed 0.95 the speed of light) convey much more energy than a gamma photon, but less energy than a proton at the same speed (since the proton mass is much larger).

The average wave energy is then the product of the average particles number by the energy of the single particle.

A further complication is implied, when particles at speeds very near to the speed of light are considered, is that they can transform one into the other due to the relativistic equivalence of mass and energy. A good example is the X rays emission of relativistic electrons in a synchrotron or the decay of an andron into lighter particles into an andron collider.

However this get us too far I think :-)

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13y ago

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