1. (5pts) Ch. 6, problem 3 Show directly that the trial wave function 4(x,t) = A...
PrOBleM: SoLuTiONS To THE WAvE EQuATION a) By direct substitution determine which of the following functions satisfy the wave equation 1. g(z, t)-A cos(kr - wt) where A, k, w are positive constants 2. h(z,t)-Ae-(kz-wt)2 where A, k, ω are positive constants 3. p(x, t) A sinh(kx-wt) where A, k,w are positive constants 4. q(z, t) - Ae(atut) where A,a, w are positive constants 5. An arbitrary function: f(x, t) - f(kx -wt) where k and w are positive constants....
check whether the function E(x,t)= Asin(kx^2-wt^2) satisfies the wave equation. if so, find the wave speed. if not explain
Can you do (b) and (c) only thank you PrOBleM: SoLuTiONS To THE WAvE EQuATION a) By direct substitution determine which of the following functions satisfy the wave equation 1. g(z, t)-A cos(kr - wt) where A, k, w are positive constants 2. h(z,t)-Ae-(kz-wt)2 where A, k, ω are positive constants 3. p(x, t) A sinh(kx-wt) where A, k,w are positive constants 4. q(z, t) - Ae(atut) where A,a, w are positive constants 5. An arbitrary function: f(x, t) -...
a) By direct substitution determine which of the following functions satisfy the wave equation. 1. g(x, t) = Acos(kx − t) where A, k, are positive constants. 2. h(x, t) = Ae where A, k, are positive constants. 3. p(x, t) = Asinh(kx − t) where A, k, are positive constants. 4. q(x, t) = Ae where A, a, are positive constants. 5. An arbitrary function: f(x, t) = f(kx−t) where k and are positive constants. (Hint: Be careful with...
Consider the following wave function: y(x, t) = cos(kx - omega t). a. Show that the above function is an eigenfunction of the operator partialdifferential^2/partialdifferential x^2[...] and determine its eigenvalue. b. Show that the above function is a solution of the wave equation expressed as partialdifferential^2 y(x, t)/partialdifferential x^2 = 1/v^2 partialdifferential^2 y(x, t)/partialdifferential t^2, given the wave velocity is v = omega/k (where omega = 2 pi V and k = 2pi/lambda).
P(x,t) = Aeixe-ißt a) Show that the above function is a wave by showing that it satisfies the wave equation. A, a, B are arbitrary constants, i is the unit imaginary number. b) Find the wave speed where a = 1, B = 4, and A-3.
P(x,t) = Aeixe-ißt a) Show that the above function is a wave by showing that it satisfies the wave equation. A, a, B are arbitrary constants, i is the unit imaginary number. b) Find the wave speed where a = 1, B = 4, and A-3.
7. (Problem 7.1) A string is oscillating with the wave function y(x,t) A sin(kx-wt) with A-3 cm, k=0.2π rad/cm, and ω = 10π rad/cm. For both t = 0.05s and 0.07s sketch the string for 0 s xS 10 cm
Problem 3 Consider a possible solution to Maxwell's equations in vacuum given by A(x, t) = Ao exp(i(kx - wt)), V(x, t) = 0 where A is the vector potential and V is the scalar potential. Suppose Ao, k and w are constants in space and time. a) Compute the time-dependent electric and magnetic fields from the given potentials. Show your work. b) Give the contraints, if any, on Ao, k and w imposed by the following two Maxwell's equations...
The wave equation can be written as:∂^2 y/∂x^2 = 1/v^2 (∂^2 y /∂t^2) where y = y(x,t) has units of meters, x is also in meters, and t is in seconds. (a) Show explicitly that the function y(x,t) = ymsin(kx)cos(wt) satisfies the wave equation (6 points). (b) Is the function for y = y(x,t) describe a traveling wave? You must explain your answer to get full credit (2 points). 8. On a winter day with a temperature of Tc, the...