15. Propagation guidée des ondes

CODE :

In [1]:

# Importation des modules
import numpy as np
import numpy.random as npr
import matplotlib.pyplot as plt
import pandas as pd
from scipy.optimize import curve_fit,leastsq
#%matplotlib qt

Fibre optique¶

In [2]:

nc = 1.51
ng = 1.33
alpha_lim_th = np.arcsin(np.sqrt(nc**2 - ng**2))*180/np.pi
print("L'angle d'incidence limite dans la fibre est",np.round(alpha_lim_th),'+/- 5 °')

L'angle d'incidence limite dans la fibre est 46.0 +/- 5 °

Tube acoustique¶

In [7]:

f = 40e3
td = 123e-6 # offset sur le temps due au temps de réponse du récepteur
T = 293
c = np.sqrt(1.4*8.314*T/29e-3) # Vitesse du son dans l'air
lam = c/f

uc = 1
ulam = 0.1e-3

def vg(L,dt):
    return L/dt

def lambdag(v):
    return c*lam/v

#def mu(lamg,a):
#    return np.sqrt((1/lam**2)-(1/lamg**2))*2*np.pi*a

In [9]:

d1 =  # diamètre du tube
a1 = d1/2
L1 = # Longeur du tube

# incertitudes
uL = 
udt = 
ua = 

# Dataframe
df1 = pd.DataFrame({'dt [ms]' : [5.07, 6.36]},
                  index = [1, 2],
                  columns = ['dt [ms]'])

df1['dt [s]'] = [df1['dt [ms]'][i]*1e-3-td for i in df1.index]

df1['vg [m/s]'] = [vg(L1,df1['dt [s]'][i]) for i in df1.index]
df1['uvg [m/s]'] = [df1['vg [m/s]'][i]*np.sqrt((uL/L1)**2 + (udt/df1['dt [s]'][i])**2) for i in df1.index]

df1['lambdag [m]'] = [lambdag(df1['vg [m/s]'][i]) for i in df1.index]
df1['ulamdag [m]'] = [df1['lambdag [m]'][i]*np.sqrt((uc/c)**2 + (ulam/lam)**2 + (df1['uvg [m/s]'][i]/df1['vg [m/s]'][i])**2) for i in df1.index]

#df1['mu'] = [mu(df1['lambdag [m]'][i],a1) for i in df1.index]
#df1['umu'] = [df1['mu'][i] * ((ua/a1) + ((2/(1/lam**2-1/df1['lambdag [m]'][i]))*((ulam/lam**3) + (df1['ulamdag [m]'][i]/df1['lambdag [m]'][i]**3)))) for i in df1.index]

#print(df1)
#print("Les modes se propageant sont ceux associés au valeurs de mu :",round(df1['mu'][1],2),"+/-",round(df1['umu'][1],2),"et",round(df1['mu'][2],2),"+/-",round(df1['umu'][2],2))

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Date de dernière mise à jour : 07/06/2025