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
check whether the function E(x,t)= Asin(kx^2-wt^2) satisfies the wave equation. if so, find the wave speed....
Does the superposition (x, t) Asin (kx-wt) + 2A sin(kx + ω) generate a standing wave? Answer this question by using trigonometric identities to combine the two terms. 7.
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
2. Determine whether the following function satisfies the wave equation. v(x,t)= 4e(in-a)
2. Determine whether the following function satisfies the wave equation. Y(x,t)= Ae (kr-at)
If we have a position wave function y(x, t) = Acos(kx - wt), and we rely on the second derivate of this function to find the maximum transverse acceleration of particles on a rope, would we use amax = Aw2 or amax = - Aw2, since the second derivative would retain the minus sign?
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.
B(, t) = Bmar sin(kx - wt). (e) Using Faraday's law, find the electric field induced by the magnetic wave. (f) In part (e), what is the amplitude of the electric wave? Is there any phase difference between the electric wave and the magnetic wave? (g) The electric field you found in part (e) should also satisfy Ampére-Maxwell equation. Find the speed of the EM wave in terms of the constants en and yo using this requirement.
E=sin(kx-wt) z.
and B=-sin(kx-wt) y.
z and y are unit vector and this means EM wave
propagates along x axis.
what is gonna be the E field B field equation when it propagates
with 45 degree on xy plane like picture??
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
Prove that E(x,t) = E0ei(kx-ωt) is a solution to the wave equation.