Problem 3. Wavier than a Waving...Wave Demonstrate that the following is a wave function, E(y,t)-Egeky) What...
Demonstrate that the following is a wave function, E(v,t) Eeiby-) What is the velocity of this wave?
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...
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
The wave of a plucked, taut-wire is represented by the function, y(x, t) = 3/[(x – 2.0t)2 + 1]. a) Sketch the amplitude of the wave pulse as a function of position for t=0 s, t = 1.0 s, t = 2.0 s. b) The displacement of a wave is given by the expression, y (x, t) = 15cos(1.0x – 100xt). The wavelength is measured to be 2n m. Determine the wavenumber of this wave. c) Sketch the wavefronts of...
A transverse wave on a string is described by the following wave function. Y = 0.095 sin (1x + 5nt) where x and y are in meters and t is in seconds. (a) Determine the transverse speed at t = 0.300 s for an element of the string located at x = 1.30 m m/s (b) Determine the transverse acceleration at t = 0.300 s for an element of the string located at x + 1.30 m. m/s2 (c) What...
A transverse wave on a string is modeled with the wave function y(x, t) (0.80 m)sin[(0.85 m)x (1.70 s)t 0.20]. (Indicate the direction with the signs of your answers.) (a) Find the wave velocity (in m/s). m/s (b) Find the position (in cm) in the y-direction, the velocity (in cm/s) perpendicular to the motior of the wave, and the acceleration (in cm/s2) perpendicular to the motion of the wave of a small segment of the string centered at x 0.40...
1. Demonstrate that E-Eo cos (ω (t-u)) and E-Eelu(t-z) are solutions to the E-field wave equation.
A propagating wave is described by the wave function (in SI units) y(x, t) = 3 sin(4.x + 2.t) What can be said about the direction of wave propagation and its speed (assume positive x direction is to the right)? o Wave propagates to the left with the speed of 0.5 m/s o Wave propagates to the right with the speed of 0.5 m/s o Wave propagates to the left with the speed of 2 m/s o Wave propagates to...
A wave is modeled with the function y ( x , t ) = 0 . 2 5 cos ( 0 . 3 0 x − 0 . 9 0 t + π/ 3 ) where all lengths are in meters and all times in seconds. a. Find the wavelength of the wave. b. Find the period of the wave. c. Find the wave speed (a positive number). d. What is the instantaneous velocity of one of the particles that...