This page was generated from doc/examples/animations-pulsating-sphere.ipynb. Interactive online version:

Animations of a Pulsating Sphere

import sfs
import numpy as np
import matplotlib.pyplot as plt
from IPython.display import HTML

In this example, the sound field of a pulsating sphere is visualized. Different acoustic variables, such as sound pressure, particle velocity, and particle displacement, are simulated. The first two quantities are computed with

• sfs.fd.source.pulsating_sphere() and

• sfs.fd.source.pulsating_sphere_velocity()

while the last one can be obtained by using

• sfs.fd.displacement()

which converts the particle velocity into displacement.

A couple of additional functions are implemented in

• animations_pulsating_sphere.py

in order to help creating animating pictures, which is fun!

import animations_pulsating_sphere as animation

# Pulsating sphere
center = [0, 0, 0]
radius = 0.25
amplitude = 0.05
f = 1000  # frequency
omega = 2 * np.pi * f  # angular frequency

# Axis limits
figsize = (6, 6)
xmin, xmax = -1, 1
ymin, ymax = -1, 1

# Animations
frames = 20  # frames per period

Particle Displacement

grid = sfs.util.xyz_grid([xmin, xmax], [ymin, ymax], 0, spacing=0.025)
ani = animation.particle_displacement(
        omega, center, radius, amplitude, grid, frames, figsize, c='Gray')
plt.close()
HTML(ani.to_jshtml())

Once Loop Reflect

Click the arrow button to start the animation. to_jshtml() allows you to play with the animation, e.g. speed up/down the animation (+/- button). Try to reverse the playback by clicking the left arrow. You’ll see a sound sink.

You can also show the animation by using to_html5_video(). See the documentation for more detail.

Of course, different types of grid can be chosen. Below is the particle animation using the same parameters but with a hexagonal grid.

def hex_grid(xlim, ylim, hex_edge, align='horizontal'):
    if align is 'vertical':
        umin, umax = ylim
        vmin, vmax = xlim
    else:
        umin, umax = xlim
        vmin, vmax = ylim
    du = np.sqrt(3) * hex_edge
    dv = 1.5 * hex_edge
    num_u = int((umax - umin) / du)
    num_v = int((vmax - vmin) / dv)
    u, v = np.meshgrid(np.linspace(umin, umax, num_u),
                       np.linspace(vmin, vmax, num_v))
    u[::2] += 0.5 * du

    if align is 'vertical':
        grid = v, u, 0
    elif align is 'horizontal':
        grid = u, v, 0
    return  grid

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  if align is 'vertical':
/tmp/ipykernel_1294/2319301824.py:16: SyntaxWarning: "is" with 'str' literal. Did you mean "=="?
  if align is 'vertical':
/tmp/ipykernel_1294/2319301824.py:18: SyntaxWarning: "is" with 'str' literal. Did you mean "=="?
  elif align is 'horizontal':

grid = sfs.util.as_xyz_components(hex_grid([xmin, xmax],
                                           [ymin, ymax],
                                           0.0125,
                                           'vertical'))
ani = animation.particle_displacement(
        omega, center, radius, amplitude, grid, frames, figsize, c='Gray')
plt.close()
HTML(ani.to_jshtml())

Once Loop Reflect

Another one using a random grid.

grid = sfs.util.as_xyz_components([np.random.uniform(xmin, xmax, 4000),
                                   np.random.uniform(ymin, ymax, 4000),
                                   0])
ani = animation.particle_displacement(
        omega, center, radius, amplitude, grid, frames, figsize, c='Gray')
plt.close()
HTML(ani.to_jshtml())

Once Loop Reflect