show the velocity and direction while proving that s(x,t) = Aexp[-(4x+6t)^2] is a wave equation

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genius_generous answered 1 year ago

Show that in Lorentz gauge the electric potential ?(x, t) satisfies the wave equation.

Tom is on board a bus moving with a constant velocity in the +x direction while...

Tom is on board a bus moving with a constant velocity in the +x direction while Fred is standing on the sidewalk. When the Bus passes Fred, Tom tosses a coin and catches it on its way back. Both Fred and Tom measure the time interval for the coin toss. Which of the following observations is correct? A. Tom will measure a longer time interval for the coin toss and observe that the coin follows a parabolic path. B. Fred will...

x"(t)- 4x'(t)+4x(t)=4e^2t ; x(0)= -1, x'(0)= -4

Solve the following differential equations: 1.) y"(t)- 6 y'(t)+9 y(t)=6t^2e^(3t) ; y(0)=y'(0)=0 2.)x"(t)+4x(t)=t +4 ; x(0)=1...

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The displacement of a wave traveling in the negative x-direction is y(x,t)= ( 5.2 cm )cos(...

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Solve the wave equation ∂2u/∂t2 = 4 ∂2u/∂x2 , 0 < x < 2, t >...

Solve the wave equation ∂2u/∂t2 = 4 ∂2u/∂x2 , 0 < x < 2, t > 0 subject to the following boundary and initial conditions. u(0, t) = 0, u(2, t) = 0, u(x, 0) = { x, 0 < x ≤ 1 2 − x, 1 < x < 2 , ut(x, 0) = 0

A block of 4 kg moves in the +x direction with a velocity of 15 m/s...

A block of 4 kg moves in the +x direction with a velocity of 15 m/s while a block of 6 kg moves in the +y direction with a velocity of 10 m/s. They collide and stick together. Calculate the following: a. What is the momentum in this system? b. What is the final velocity of the two blocks?

A particle leaves the origin with an initial velocity of 4.10 m/s in the x direction,...

A particle leaves the origin with an initial velocity of 4.10 m/s in the x direction, and moves with constant acceleration ax = -1.40 m/s2 and ay = 3.80 m/s2. How far does the particle move in the x direction before turning around? What is the particle's velocity at this time? Enter the x component first, followed by the y component.

derive the classical wave equation. Show the relationship between this equation and the electromagnetic wave equation.

Find the derivative of the parametric curve x = 6t - t^2, y = lnt where...

Find the derivative of the parametric curve x = 6t - t^2, y = lnt where t > 0 A. Find all values of t where the tangent line is horizontal. After you find the values of t where the tangent lines are horizontal, find the corresponding x and y values giving your answers as ordered pairs. B. Find all values of t where the tangent line is vertical. After you find the values of t where the tangent lines...

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