Show that the wave fucntion y=e^b(x-vt) is solution to linear wave equation(i.e d2y/dx2=1/v^2 d2y/dt2?
where d is partial derivative

Question

Show that the wave fucntion y=e^b(x-vt) is solution to linear wave equation(i.e d2y/dx2=1/v^2 d2y/dt2?
where d is partial derivative

irishboy123 · Answer

just plug it in, eg $y_t = -vb e^{b(x-vt)}$, and then add it all up...

anonymous · Answer

plz explain with steps sir if possible

anonymous · Answer

i dont know much about derivatives and integrals

irishboy123 · Answer

lol!  

seriously, if you don't know that *much about* calculus, messing about with the wave equation is a tough one for anyone :p 

you have $y_t$ which to be clear is a simpler way of writing $\frac{∂y}{∂t}$.  now do $y_{tt}$, ie$\frac{∂^2y}{∂t^2}$.  just pattern match and see where you go!

in terms of the x partial, you have: $y_x =be^b(x-vt)$.  do the same again to get $y_{xx} $