Wave Interference Pattern using Python

 

import matplotlib.pyplot as plt

import numpy as np

from mpl_toolkits.mplot3d import Axes3D

x=np.linspace(-10,10,300)

y=np.linspace(-10,10,300)

X,Y=np.meshgrid(x,y)

r1=np.sqrt((X+3)**2+(Y+3)**2)

r2=np.sqrt((X-3)**2+(Y-3)**2)

Z=np.sin(r1)+np.sin(r2)

fig=plt.figure(figsize=(10,6))

ax=fig.add_subplot(111,projection='3d')

ax.plot_surface(X,Y,Z,cmap='viridis',edgecolor='none')

ax.set_title("3D Wave Interferance Surface")

plt.show()

#source code --> clcoding.com 

Code Explanation:

1. Import Required Libraries

import numpy as np

import matplotlib.pyplot as plt

from mpl_toolkits.mplot3d import Axes3D

NumPy: Used for numerical calculations, array manipulations, and math functions.

 

Matplotlib: Used to create static, animated, or interactive plots.

 

Axes3D: Enables 3D plotting features in Matplotlib.

 

 2. Define Grid Range for X and Y Axes

x = np.linspace(-10, 10, 300)

y = np.linspace(-10, 10, 300)

X, Y = np.meshgrid(x, y)

np.linspace(...) creates 300 evenly spaced values from -10 to 10.

 

np.meshgrid(...) creates 2D grid coordinates from 1D x and y arrays for surface plotting.

 

 

 3. Calculate Distance from Two Wave Sources

r1 = np.sqrt((X + 3)**2 + (Y + 3)**2)

r2 = np.sqrt((X - 3)**2 + (Y - 3)**2)

r1: Distance from wave source 1 at point (-3, -3).

 

r2: Distance from wave source 2 at point (3, 3).

 

This is based on the Euclidean distance formula.

 

 4. Compute Interference Pattern (Z-axis Height)

Z = np.sin(r1) + np.sin(r2)

Simulates two wave fronts overlapping.

 

Adds sine waves from both sources to get constructive and destructive interference.

 

Result: Ripple-like surface of varying height values.

 

5. Create a 3D Plot Figure

fig = plt.figure(figsize=(10, 6))

ax = fig.add_subplot(111, projection='3d')

fig: Initializes the figure (canvas).

 

figsize: Width = 10 inches, Height = 6 inches.

 

ax: Adds a single 3D subplot for plotting the surface.

 

6. Plot the 3D Surface

ax.plot_surface(X, Y, Z, cmap='viridis', edgecolor='none')

Renders the 3D surface using the X, Y, and Z values.

cmap='viridis': Applies a smooth color gradient.

edgecolor='none': Removes mesh edges for a cleaner look.

 

7. Set Plot Title and Display

ax.set_title("3D Wave Interference Surface")

plt.show()

Adds a title to the plot.

plt.show() displays the plot window with the 3D surface.