Momentum and Energy of Waves

Abstract

Elementary arguments of conservation of energy and momentum are used to derive expressions for what Sturrock terms the ``formal'' momentum, angular momentum, and energy of a plane wave in a moving medium. If E is the energy per unit length, p the momentum per unit length, q the angular momentum per unit length, vf the phase velocity, and if the angular variation of a circulatory polarized wave is as exp(—jnθ), p=E/vf,q=nE/ω.If E0 is the energy per unit length observed moving with the medium, and then if the medium moves past the observer with a velocity u and the observer measures a phase velocity vf, he observes an energy per unit length E, E=E0/(1−u/vf). When p, q, and E are not the physical momenta and energy, they lead to the correct power and force for sinusoidal sources moving with respect to the medium.