Determine if the functionD = A sin kx cos ωt is a solution of the wave...
Determine if the functionD = A sin kx cos ωt is a solution of
the wave equation. (Must show your proof, no
credit given without correct work.)
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Determine if the functionD = A sin kx cos ωt is a solution of
the wave...
Prove that E(x,t) = E0ei(kx-ωt) is a solution to the wave equation.
Prove that E(x,t) = E0ei(kx-ωt) is a solution to the wave equation.
Consider a wave that is represented by ψ(x, t) = 4 cos (kx − ωt). where...
Consider a wave that is represented by ψ(x, t) = 4 cos (kx − ωt). where k = 2π/λ and ω = 2πf. The aim of the following exercises is to show that this expression captures many of the intuitive features of waves. a) Consider a snapshot of the wave at t = 0. Use the expression to find the possible values of x at which the crests (maximum points) of the wave are located. By what distance are neighboring...
A sound wave of the form s = sm cos(kx - ωt + φ) travels at...
A sound wave of the form s = sm cos(kx - ωt + φ) travels at 343 m/s through air in a long horizontal tube. At one instant, air molecule A at x = 2.04 m is at its maximum positive displacement of 6.20 nm and air molecule B at x = 2.08 m is at a positive displacement of 2.00 nm. All the molecules between A and B are at intermediate displacements. What is the frequency of the wave?
1. A common solution to the wave equation is E(x,t) = A Cos(kx-wt). On paper take...
1. A common solution to the wave equation is E(x,t) = A Cos(kx-wt). On paper take the needed derivatives and show that it actually is a solution. 2. A common solution to the wave equation is E(x,t) = A ei(kx+wt). On paper take the needed derivatives and show that it actually is a solution. Note that i is the square-root of -1
Which of the following is/are solution to the wave equation, 1. ei(kx-wt) a. b. (cos kx)...
Which of the following is/are solution to the wave equation, 1. ei(kx-wt) a. b. (cos kx) (sin ot) sin et C. e sin (kx - t) d. e COs t e. e 2. A building made with a steel structure is 650 m high on a winter day when the temperature is 0° F. How much taller (in cm) is the building when it is 100° F? (The linear expansion coefficient of steel is 11 x 10 (C) ) A...
Show that sin (kx) and cos (kx) given in Eq. (11-48a) are two independent solutions of...
Show that sin (kx) and cos (kx) given in Eq. (11-48a) are two independent solutions of the differentia equation, Eq. (11-47a). Consider a rectangular wavequide haing dimoneinc 404 We were unable to transcribe this image(11-48a) X(x)- Asin(k,x)+B cos (k,x)
Show that the wavefunction Ѱ = C sin (kx) is a solution of the following Schrödinger’s...
Show that the wavefunction Ѱ = C sin (kx) is a solution of the
following Schrödinger’s equation where V0 is a constant. What is
the energy corresponding to this wavefunction? (14 marks)
Calculate the probability density given by the wavefunctions for
the groud state, first and second excited states. (6
marks)
a) Show that the wavefunction ) = C sin(kx) is a solution of the following Schrödinger's equation h2 d2 2m dx2 V = Et where V is just a...
Consider the following wave function: y(x, t) = cos(kx - omega t). a. Show that the...
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).
A good definition of a “wave” is a disturbance of a continuous medium that propagates with...
A good definition of a “wave” is a disturbance of a continuous medium that propagates with a fixed shape at constant velocity. (Griffiths, 1999, Introduction to Electrodynamics). Another way of saying this is the medium (e.g. a string, water, or air) will only propagate a wave as long as its shape satisfies the wave equation: d^2 f/dx^2 =1/v^2 . d^2 f/dt^2 a) Show explicitly whether the displacement function f(x,t) = A sin(kx) cos(ωt) will be propagated in a medium as...
Question 21 (3 points) Saved day Which of the following is a solution to the wave...
Question 21 (3 points) Saved day Which of the following is a solution to the wave equation, aly dt2 Oy = e-* sin (kx – wt) Oy = (cos kx) (sin t) Oy = e-* sin at y = esin x Oy = e-* cost Actually, all of these are solutions to the wave equation. Actually, none of the above is a solution to the wave equation.
Which of the following is/are solution to the wave equation, 1. ei(kx-wt) a. b. (cos kx) (sin ot) sin et C. e sin (kx - t) d. e COs t e. e 2. A building made with a steel structure is 650 m high on a winter day when the temperature is 0° F. How much taller (in cm) is the building when it is 100° F? (The linear expansion coefficient of steel is 11 x 10 (C) ) A...
Show that sin (kx) and cos (kx) given in Eq. (11-48a) are two independent solutions of the differentia equation, Eq. (11-47a). Consider a rectangular wavequide haing dimoneinc 404 We were unable to transcribe this image(11-48a) X(x)- Asin(k,x)+B cos (k,x)
Show that the wavefunction Ѱ = C sin (kx) is a solution of the
following Schrödinger’s equation where V0 is a constant. What is
the energy corresponding to this wavefunction? (14 marks)
Calculate the probability density given by the wavefunctions for
the groud state, first and second excited states. (6
marks)
a) Show that the wavefunction ) = C sin(kx) is a solution of the following Schrödinger's equation h2 d2 2m dx2 V = Et where V is just a...
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).
Question 21 (3 points) Saved day Which of the following is a solution to the wave equation, aly dt2 Oy = e-* sin (kx – wt) Oy = (cos kx) (sin t) Oy = e-* sin at y = esin x Oy = e-* cost Actually, all of these are solutions to the wave equation. Actually, none of the above is a solution to the wave equation.
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