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Onedimensional lossless wave equation:
Plug in traveling wave to the right:
 Given
, the wave equation is satisfied for
any shape traveling to the right at speed
(but remember slope
)
 Similarly, any leftgoing traveling wave at speed
,
, satisfies the wave equation (show)
 General solution to lossless, 1D, secondorder wave equation:

and
are arbitrary twicedifferentiable
functions (slope
)
 Important point: Function of two variables
is replaced by two
functions of a single (time) variable
reduced
computational complexity.
 Published by d'Alembert in 1747
(wave equation itself introduced in same paper)
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Download StringWaves.pdf
Download StringWaves_2up.pdf
Download StringWaves_4up.pdf