Assume the well known PDE of an infinite length string(adsbygoogle = window.adsbygoogle || []).push({});

D^2(y)/Dt^2 = c^2* ( D^2(y)/Dx^2)

where y=y(x,t) is the transverse displacement of the string.

D/Dx= partial derivative with respect to x

D/Dt= partial derivative with respect to t

c= velocity of the wave

According to Morse and Ingard's Theoretical Acoustics (page 97), if the shape of the string is described by the function y(x,t)=F(x-ct), then Dy/Dt= -c*F'(x-ct)= -c*Dy/Dx (Where F'(z)= the derivative of F with respect to z).

I found the last statement a little bit confusing. Could anyone explain why F'(x-ct)=Dy/Dx ? Obviously if F'(x-ct)=Dy/Dt then a constrain is put on c which is not correct...

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# Wave equation for a string

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