well, for a plane wave
d^2y/dx^2 must be (1/v^2)d^2y/dt^2
if y = x^2 + v^2 t^2
dy/dx = 2x
d^2y/dx^2 = 2
dy/dt = 2 v^2 t
d^2y/dt^2 = 2 v^2
so it is not and you should have written
x^2 + (1/v^2) t^2
Show that the function y(x,t) = X^2 + V^2t^2 is a solution of the general wave equation.
2 answers
sorry, no it is ok
well, for a plane wave
d^2y/dx^2 must be (1/v^2)d^2y/dt^2
if y = x^2 + v^2 t^2
dy/dx = 2x
d^2y/dx^2 = 2
dy/dt = 2 v^2 t
d^2y/dt^2 = 2 v^2
2 = (1/v^2) 2 v^2
well, for a plane wave
d^2y/dx^2 must be (1/v^2)d^2y/dt^2
if y = x^2 + v^2 t^2
dy/dx = 2x
d^2y/dx^2 = 2
dy/dt = 2 v^2 t
d^2y/dt^2 = 2 v^2
2 = (1/v^2) 2 v^2