(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Because q(x,t) = A*exp[-(x-ct)^{2}/σ^{2}] is a function of x-ct, it is a solution to the wave equation (on an infinite domain).

(a) What are the initial conditions [a(x) and b(x)] that give rise to this form of q(x,t)?

(b) if f(x) is constant, then Eq. (2) shows that solution is only a function of x-ct. For the condition that f(x) is constant find b(x) in terms of a(x). [Hint: consider eq. (3a)]

(c) Show that the initial conditions you found in part (a) satisfy the relationship that you found in part (b).

2. Relevant equations

Initial displacement: a(x) = q(x,0)

Initial velocity: b(x) = [itex]dq(x,0)/dt[/itex] (this should be a partial derivative--sorry)

Eq 2: q(x,t) = f(x+ct) + g(x-ct)

Eq 3a: f(x) = [itex]1/2[/itex] (a(x) + [itex]\frac{1}{c}[/itex] ∫b(x')dx') where the integral is from x_{0}to x) (sorry again...)

3. The attempt at a solution

Okay, for part (a), I just used the given q(x,t) to solve for the boundary conditions a(x) and b(x), and I got

a(x) = A*exp(-x^{2}/σ^{2})

b(x) = (2cx/σ^{2})*A*exp(-x^{2}/σ^{2})

For part (b), I'm a little stumped at the moment. Can I just solve for b(x) in equation (3a)...? I'm not sure how I would go about doing that with b(x) inside the definite integral.

I think (c) will be apparent once I figure out (b). A little push in the right direction would be much appreciated! Thanks!!!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Boundary conditions of solution to the wave equation

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**