01.Animation_Play_in_3D_Frequency_vs_Tension_and_Wave_Speed_2.py

import numpy as np
import pandas as pd
import plotly.express as px

# Constants and variables
mu = 0.03
length = 2.0
tension_values = np.linspace(10, 40, 100)

# Mathematical expressions
tension, wave_speed, frequency = symbols('tension wave_speed frequency')
wave_speed_eq = Eq(wave_speed, sqrt(tension / mu))
frequency_eq = Eq(frequency, wave_speed / length)

# Data generation and DataFrame
wave_speeds = [float(solve(wave_speed_eq.subs(tension, t))[0]) for t in tension_values]
frequencies = [float(solve(frequency_eq.subs(wave_speed, ws))[0]) for ws in wave_speeds]
results_df = pd.DataFrame({'Tension (N)': tension_values, 'Wave Speed (m/s)': wave_speeds, 'Frequency (Hz)': frequencies})

# Create an animated scatter plot using Plotly Express
fig = px.scatter(results_df, x='Tension (N)', y='Wave Speed (m/s)', animation_frame='Tension (N)',
                 animation_group='Tension (N)', size='Frequency (Hz)', color='Frequency (Hz)',
                 title='Frequency vs. Tension and Wave Speed Animation',
                 labels={'Tension (N)': 'Tension (N)', 'Wave Speed (m/s)': 'Wave Speed (m/s)', 'Frequency (Hz)': 'Frequency (Hz)'},
                 hover_name='Tension (N)')

# Customize animation settings
fig.update_traces(marker=dict(size=8), selector=dict(mode='markers'))

# Add axis labels and ranges
fig.update_layout(scene=dict(xaxis_title='Tension (N)', yaxis_title='Wave Speed (m/s)', zaxis_title='Frequency (Hz)'),
                  margin=dict(l=0, r=0, b=0, t=40))

# Show interactive animation
fig.show()