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A plane wave in free space is transverse in both fields because

  • A.the medium cannot support a longitudinal field
  • B.the frequency is too high for a longitudinal component to follow
  • C.the intrinsic impedance is purely real
  • D.the two divergence equations forbid a component along the direction of travel

Answer: D

Applying the divergence conditions to a field varying only along the direction of propagation forces the component in that direction to be constant, and it must therefore be zero for a wave. This is why an electromagnetic wave can be polarised while a sound wave cannot.

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