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Project: My Project
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Kernel: Python 3 (system-wide)

Importing necessary libraries

We'll need numpy for mathematical functions and matplotlib for plotting the 3D graph.

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

Defining the wave equation

The wave equation in 3-dimensions can be represented as:

u(x,t)=Asin⁡(kx−ωt+ϕ)u(x, t) = A \sin(kx - \omega t + \phi)

Where:

  • AA is the amplitude

  • kk is the wave number

  • ω\omega is the angular frequency

  • ϕ\phi is the phase

Define the variables:

A = 1.0  # Amplitude
k = 2 * np.pi / 10  # Wave number
omega = 2 * np.pi / 5  # Angular frequency
phi = 0  # Phase

Generating the grid

Create a grid for xx and tt:

x = np.linspace(0, 10, 100)
t = np.linspace(0, 5, 100)
x, t = np.meshgrid(x, t)

Defining the wave function

Calculate the wave function u(x,t)u(x, t):

u = A * np.sin(k * x - omega * t + phi)

Plotting the wave equation

Create a 3D plot of the wave equation:

fig = plt.figure(figsize=(10, 7))
ax = fig.add_subplot(111, projection='3d')
ax.plot_surface(x, t, u, cmap='viridis')
ax.set_title('3D Plot of the Wave Equation')
ax.set_xlabel('x')
ax.set_ylabel('t')
ax.set_zlabel('u(x, t)')
plt.show()
Image in a Jupyter notebook
a=2
b=3
b-a
Intro

  • σ−ν=γ\sigma-\nu=\gamma