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In [1]:

    
%matplotlib inline

import numpy as np
from matplotlib import style
import matplotlib.pyplot as plt

style.use('fivethirtyeight')

Que tipo de onde seria essa? Lembre-se sempre de checar h/L!



In [2]:

    
twopi = 2.0 * np.pi
x = 0.0
No = 10
L = 200
K = 2 * np.pi / L
H = 10.
g = 9.8

w = np.sqrt(g * K ** 2 * H)  # FIXME!
T = 2 * np.pi / w
t = twopi * np.linspace(0, T, 100)



In [3]:

    
HoL = H/L
HoL









    Out[3]:





0.05

Using 10% of difference in $\delta k$ and $\delta \omega$.

Play with dk and dw and report the differeces you see.



In [4]:

    
dk = 0.1 * K
dw = 0.1 * w

Using the equations from our notes:

$\eta_1 = \eta_o \cos[(K + \delta k)x - (\omega + \delta\omega)t]$

$\eta_2 = \eta_o \cos[(K - \delta k)x - (\omega - \delta\omega)t]$



In [5]:

    
eta_1 = No * np.cos((K + dk) * x - (w + dw) * t)
eta_2 = No * np.cos((K - dk) * x - (w - dw) * t)



In [6]:

    
fig, (ax0, ax1, ax2) = plt.subplots(nrows=3, ncols=1, figsize=(5, 3.15), sharex=True, sharey=True)

kw = dict(linewidth=2)

label0 = r'$\eta_1 = \eta_o \cos[(K + \delta k)x - (\omega + \delta\omega)t]$'
label1 = r'$\eta_2 = \eta_o \cos[(K - \delta k)x - (\omega - \delta\omega)t]$'
label2 = r'$\eta_1 + \eta_2$'

ax0.plot(t, eta_1, color='darkgreen', label=label0, **kw)
ax1.plot(t, eta_2, color='darkorange', label=label1, **kw)

ax1.text(0.45, 1, '+', transform=ax1.transAxes)

ax2.plot(t, eta_1 + eta_2, color='cornflowerblue', label=label2, **kw)

ax2.text(0.45, 1, '=', transform=ax2.transAxes)

ax0.axis('off')
ax1.axis('off')
ax2.axis('off')

x, y = 0.95, 1.025
ax0.text(x, y, label0, transform=ax0.transAxes)
ax1.text(x, y, label1, transform=ax1.transAxes)
ax2.text(x, y, label2, transform=ax2.transAxes)


fig.savefig("wave_interaction.svg", bbox_inches='tight')