Show that for any differentiable function g(τ), u(x, z, t) = g(t − px − ηz), where p is a constant and η = /v 2 − p2, satisfies the 2d wave equation ∂2u+∂2u= 1 ∂2u. ∂x2 ∂z2 v2 ∂t2 also show that u(x, z, t) is a plane wave traveling at a horizontal (x-direction) slowness of p.

answer: 12

step-by-step explanation:

because yes

step-by-step explanation:

step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)