I need help with d) please help thank you
I need help with d) please help thank you Question 1 Wave motion appears in all branches of physics. In the lectures we...
1. Let u be a solution of the wave equation u 0. Let the points A, B, C, D be the vertices of the paralleogram formed by the two pairs of characteristic lines r-ctC1,x- ct-2,+ ct- di,r +ct- d2 Show that u (A)+u (C)-u (B) + u (D Use this to find u satisfying For which (x, t) can you determine u (x, t) uniquely this way? 2. Suppose u satisfies the wave equation utt -curr0 in the strip 0...
1. Let u be a solution of the wave equation u0. Let the points A, B, C, D be the vertices of the paralleogram formed by the two pairs of characteristic lines z--d-q,z-ct-c2, z + ct = di, z + ct d2. Show that u(A) u (C) u(B) +u(D) Use this to find u satisfying till- tLzz =0, u( s,s)-s, u(8,8)-82 for s > 0. For which (r, t) can you determine u (x, t) uniquely this way? 1. Let...
d1= 3 & d2= 2 Question 2 Find the solution 11(x, 1) for the 1-D wave equation aT = (a) 25-for -o <x < oo with initial conditions it (x,0) = A (x) , where A(x) is presented in the diagram below, and zero initial velocity. For full marks u(x,t) needs to be expressed as an equation involving x and 1, somewhat similar to fex) on page 8s of the Notes Part 2. 2 d2+5 r-0 di+10 di+15 di+20 3...
Question 2 ul lu (a) Find the solution u(x,t) for the 1-D wave equationfor -oo < x < oo with initial conditions u (x,0)-A(x) , where A(x) s presented in the diagram below, and zero initial velocity. For full marks u(x,t) needs to be expressed as an equation involving x and t, somewhat similar to f(x) on page 85 of the Notes Part 2. di+10 dı+15di+20 (b) Check for the wave equation in (a) that if f(xtct) (use appropriate value...
d1=8 d2=9 lu for Find the solution u(x,t) for the l-D wave equation-=- Qx2 25 at2 (a) oo < x < oo with initial conditions u(x,0)-A(x) , where A(x) Is presented in the diagram below, and zero initial velocity. For full marks u(x,t) needs to be expressed as an equation involving x and t, somewhat similar to f(x) on page 85 of the Notes Part 2. d2+5 di+10 di+15dı+20 (b) Check for the wave equation in (a) that if (x...
Please answer question b. 4.3 In the derivation in Sect.4.1, suppose we include the effect of gravity by adding a term-Pg Ar to the discrete equation of motion (4.2), where g>O is the constant of gravitational acceleration. The wave equation is then modified to (4.48) 012 r2 = -8. 70 4 The Wave Equation Assume that x € (0,), with u satisfying Dirichlet boundary conditions at the end points. (a) Find an equilibrium solution uo(x) for (4.48), that satisfies the...
PROBLEM 4.3. The one-dimensional wave equation is ə?u - 20u = 0, ət2 or where c> 0 is constant. Show that any function of the form u(x, t) = f(x - ct)+9(2+ct), where f,g: RR are twice continuously differentiable, satisfies this equation. Explain why we call c the wave speed.
MATLAB question I need the code exactly as you would write it in MATLAB. thank you 1. Consider a Gaussian solution of the traveling-wave form ψ(z,t)-exp(-a(z-vt)2). The parameter values are a 1, 2. (a) Explain the physical meaning of these parameters (eg. what would happen if we took a = 10 instead?) Determine the direction of propagation of this solution: Is it traweling to the left or to the right? (2pts) (b) Write a Matlab code to plot the Gaussian...
*Please, answer all the literals and be detailed with the answer (do all the procedure and calculations) *Do it with a clear letter Homework (scattering) 1. Consider the time dependent Schrödinger equation written in the form where 0 2mo As it is well known the temporal evolution of a wave function ψ( t) known at a specific time t is uniquely determined for all future times t, > t as well as for all past times t' < t. Moreover,...
all parts, please For this problem, we'll solve the 3D wave equation in a box. The Laplacian in 3 dimensions is a2 vu= a2 a2 ou + ay? U= and the wave equation is 22 a2 at24 = 1 (a) (3 Points) Use separation of variables with ur,y,z,t) = S(x, y, z)T(t) to get a spatial PDE and a temporal ODE for this problem, call the separation constant A. Show all your work! (b) (3 Points) The spatial equation should...