ECE3105
Homework 2 (30 points)
Due Wed, January 30, 2019 (9 am)
Question 1 (15 points): Verify which functions are valid solutions to the 1dimensional wave equation:
(a) 𝐸 𝑥, 𝑡 = 𝐸! sin (𝑘𝑥 − 𝜔𝑡)
!
(b) 𝐸 𝑥, 𝑡 = 𝐸! 𝑒 !!(!!!!)
!
(c) 𝐸 𝑥, 𝑡 = 𝐸! 𝑒 !(!! !!!)
Where E0,α, k, ν, and ω are all constants.
!! !
! !! !
Hint: demonstrate that the following equation is true: !" ! = ! ! !" ! by taking partial
derivatives with respect to x and t of the provided functions. “u” is any property of
interest.
Question 2 (15 points): Calculate frequencies corresponding to electromagnetic
waves with wavelengths from 300 nm to 10 micron with a step of 1 nm (use a
programming tool to do this, no hand drawn graphs please):
a) show equations and units (5 points)
b) make a plot with the Y-axis: wavelength and X-axis: frequency. Your plots
MUST be clearly labeled (axis should have name of the quantity plotted and its
units) (5 points)
c) Repeat (b) but on a log scale (both axes) (5 points)