Wave Interference
What is the relationship between traveling wave and standing wave solutions to the wave equation, (
361
), in an
infinite medium? To help answer this question, let us form a superposition of two traveling wave solutions of
equal amplitude
, and zero phase angle
, that have the same wavenumber
, but are moving in opposite
directions. In other words,
(379)
Because the wave equation, (
361
), is linear, the previous superposition is a valid solution provided the two
component waves are also valid solutions: that is, provided
, which we shall assume to be the case.
Making use of the trigonometric identity
(see
Appendix
B
), the previous expression can also be written
(380)
which is a standing wave [cf., Equation (
362
)]. Evidently, a standing wave is a linear superposition of two,
otherwise identical, traveling waves that propagate in opposite directions. The two waves completely cancel one
another out at the nodes, which are situated at
, where
is an integer. This process is
known as total
destructive interference
. On the other hand, the waves reinforce one another at the antinodes,
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 Staff
 Waves And Optics, wave solutions

Click to edit the document details