Deriving equation of wave motion

  • Thread starter Pushoam
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  • #1
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The equation below (2.9) is also a linear differential equation.
This equation also describes the wave phenomena.
So, why is this equation not considered as wave equation?
I have taken it from the optics book by Chapter two Eugene Hecht,5th edition ,Pearson.
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391fdd9f-40f6-4648-874e-37d04b73169a
 
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Answers and Replies

  • #2
I must say that this is the worst derivation of the D'Alambert equation I've ever seen. It's simple but seems to describe any differentiable function. It is true that "wave" is a really general concept, in fact there are many different kind of waves and many different equation describing them, but it's not like anything is a wave!
Anyway, as the text say on page 21, you need at least a second order differential equation to describe a wave since it has in the simplest case an amplitude and a frequency, so two parameters wich requires two conditions.
 

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