## anonymous one year ago 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

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1. IrishBoy123

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

2. anonymous

plz explain with steps sir if possible

3. anonymous

i dont know much about derivatives and integrals

4. IrishBoy123

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 $$y_{xx}$$