To show that a given function is a wave function and to find the velocity of the wave represented
Demonstrate that the following is a wave function, E(v,t) Eeiby-) What is the velocity of this...
Problem 3. Wavier than a Waving...Wave Demonstrate that the following is a wave function, E(y,t)-Egeky) What is the velocity of this wave? Solution
By direct substitution, demonstrate that the following wave function for the infinite well, 2 . no is a solution of the Schrödinger equation in the case of E- 2ma2
1. Demonstrate that E-Eo cos (ω (t-u)) and E-Eelu(t-z) are solutions to the E-field wave equation.
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).
#4 3. Demonstrate that the following equations satisfy the "wave equation." For those that do, find the wave amplitude, wave speed, wavenumber, wavelength, angular frequency, and frequency in Hz? Also, denote if the wave is rightward or leftward travelling. c. y(x,t) 6cos(3x+18t) d. y(x,t) -3tan(6x+60t) yx,t) -6cos(67x)cos(80t) e. 4. For the equation given in 3(a), plot the response using a PC as a function of x over at least two full wavelengths at r-0.1 second. On a different plot, show...
2. Determine whether the following function satisfies the wave equation. v(x,t)= 4e(in-a)
If we increase the Tension (T) of a wave, the velocity of the wave increases (via v=sqrt(Tension/u)). Now using v=f*, what then happens to the frequency and wavelength? Does the frequency increase and the wavelength stay constant (or decrease)?
For waves on a string, there are two formulae for the wave velocity: v = lambda f and v = squareroot T/mu For each of the two variables T and f, answer the following: - How can you increase the value of this variable in the lab? - Explain what happens (and why) to v, lambda, mu, T, and f as a result of this change. (The length of the string is a constant.)
please help with problem (6) Use the following graph of the velocity function v(t) of an moving in a straight line to answer the following questions (a) Find the displacement of the object between t = 0 and t = 5. (b) FInd the distance traveled by the object between t = 0 and t = 5 (c) What is the position of the object at t = (d) Sketch the graph of s(t) assuming s(0) = 3. Your graph...
A sound wave traveling through water can be described by the following wave function: (x, t) = A cos (kx - omega t + pi/3) A = 0.040 m k = 1.11 rad/m omega = 1646.195 rad/s rho_water = 1.0 times 10^3 kg/m^3 a) What is the wavelength of this wave? What is the period of this wave? b) What is the amplitude of this wave? What is the phase of the wave when t = 3.0 s and x...