01.3D_Sinusoidal_Wave_I.py

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.animation as animation
import plotly.graph_objs as go
from ipywidgets import interactive, FloatSlider, HTML

# Generate pulse data
x = np.linspace(0, 10, 500)
pulse = np.exp(-0.2 * (x - 3) ** 2) * np.sin(4 * np.pi * x)

# Create pulse animation using Matplotlib
fig, ax = plt.subplots()
line, = ax.plot(x, pulse)

def animate(t):
    line.set_ydata(np.roll(pulse, int(t * 20)))
    return line,

ani = animation.FuncAnimation(fig, animate, frames=np.linspace(0, 10, 200), interval=50, blit=True)
plt.close()  # Close the initial figure

def sinusoidal_wave(x, t, A, k, omega, phi):
    return A * np.sin(k * x - omega * t + phi)

x_values = np.linspace(0, 10, 500)
t_values = np.linspace(0, 2, 200)
A = 1.0
k = 2 * np.pi / 5
omega = 2 * np.pi / 2
phi = 0.0

# Calculate wave data
wave_data = np.array([[sinusoidal_wave(x, t, A, k, omega, phi) for x in x_values] for t in t_values])

# Create an interactive HTML element for displaying information
info_text = HTML()
info_text.value = "<b>Select different parameters to visualize the wave behavior.</b>"

def plot_wave(amplitude, wave_number, angular_frequency, initial_phase):
    fig = go.Figure()

    for t in t_values:
        y_values = sinusoidal_wave(x_values, t, amplitude, wave_number, angular_frequency, initial_phase)
        fig.add_trace(go.Scatter(x=x_values, y=y_values, mode='lines', name=f't = {t:.2f}'))

    fig.update_layout(title='Interactive Sinusoidal Wave',
                      xaxis_title='x', yaxis_title='y',
                      xaxis_range=[0, 10], yaxis_range=[-1.5, 1.5],
                      annotations=[dict(text="Wavelength (λ)", x=4.5, y=-1.7, font_size=12, showarrow=False),
                                   dict(text="Amplitude (A)", x=7.5, y=1.2, font_size=12, showarrow=False)])
    fig.update_xaxes(title_text="x (Distance)")
    fig.update_yaxes(title_text="y (Amplitude)")

    info_text.value = (
        f"<b>Wave Characteristics:</b><br>"
        f"Amplitude (A): {amplitude}<br>"
        f"Wave Number (k): {wave_number:.2f}<br>"
        f"Angular Frequency (ω): {angular_frequency:.2f}<br>"
        f"Initial Phase (ϕ): {initial_phase:.2f}"
    )

    fig.show()

# Create interactive sliders for user input
interactive_plot = interactive(plot_wave,
                                amplitude=FloatSlider(min=0.1, max=2, step=0.1, value=A),
                                wave_number=FloatSlider(min=0.5, max=5, step=0.5, value=k),
                                angular_frequency=FloatSlider(min=0.5, max=5, step=0.5, value=omega),
                                initial_phase=FloatSlider(min=0, max=2 * np.pi, step=0.1, value=phi))

# Display the interactive plot and information
display(info_text)
display(interactive_plot)