Réflexion et transmission des ondes sonores

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SimulationProgrammes Python

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# -*- coding: utf-8 -*-
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"""
3
Son Monochromatique
4
O. Thual, 21/08/2021
5
"""
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#  clear all
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for iglob in list(globals().keys()):
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    if(iglob[0] != '_'):
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        exec('del {}'.format(iglob))
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# import libraries
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import numpy as np
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import matplotlib.pyplot as plt
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import os
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def inifig(xaxe=0,yaxe=0,xlab='x',ylab='y'):
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    plt.figure(2)
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    plt.axvline(xaxe)
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    plt.axhline(yaxe)
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    plt.xticks(fontsize=12)
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    plt.yticks(fontsize=12)
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    plt.xlabel(xlab,fontsize=16 )
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    plt.ylabel(ylab,fontsize=16)
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def zfi(x,le=2):
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    miss=le-len(str(x))
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    a='0'*miss+str(x)
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    return a
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def animation(name):
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    a=np.linspace(0,L,N+1);
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    acont=np.linspace(0,L,501);
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    t=0; 
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    dt=Time/Nt
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    for i in range(0,Nt):
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        title=name+" i="+zfi(i)
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        titlefig=name
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        print(title)
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        fig=plt.figure(i,figsize=(7,4))
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        plt.xlabel(r'$x$',fontsize=16 )
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        plt.ylabel(r'Pression $\widetilde p$',fontsize=16)
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        plt.title(titlefig,fontsize=16)
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        # signal
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        t=dt*i;
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        xi=signal(a,t)
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        pcont=pression(acont,t)
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        for dup in duprange:
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            plt.scatter(a+sc*xi,dup+0*xi,marker='o',color='blue',s=40)
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            amid=a[int(N/2)]; ximid=xi[int(N/2)];
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            plt.scatter(amid+sc*ximid,dup+0*ximid,marker='o',color='red',s=80)
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            #plt.scatter(a,dup+0*xi,marker='o',color='red',s=20)
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        plt.plot(acont,pcont,color='black',linewidth=3)
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        #plt.scatter(a,xi,marker='o',color='black',s=40)
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        plt.xlim(0,L)
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        plt.ylim(ymin,ymax)
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        namei=name+zfi(i)+'.png';
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        plt.grid(color='black', axis='y', linestyle='-', linewidth=1)        
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        plt.grid(color='black', axis='x', linestyle='-', linewidth=1)        
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        plt.savefig(namei)
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        plt.show()
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        plt.close()
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    gifanim="Anim"+name+".gif"
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    #os.system('/opt/local/bin/convert -set delay '+delay+' '+name+'* '+gifanim);
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    os.system('/usr/local/bin/convert -set delay '+delay+' '+name+'* '+gifanim);
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    os.system('rm '+name+'*');   
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# Main 
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F=False; T=True
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 # Progressive-cos
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if T: 
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    N=20; L=10; c=1; 
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    Nt=20; sc=1.5*L/N # scaling 
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    k=np.pi/L; omega=k*c; 
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    ymin=-1; ymax=1; Time=2*np.pi/omega
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    duprange=np.linspace(-1,1,9)
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    delay="40"
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    # signal 
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    def signal(a,t):
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        xi=np.cos(n*k*(a-c*t))
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        return xi
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    def pression(a,t):
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        p=np.sin(n*k*(a-c*t))
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        return p
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    for m in range(20,30,10):
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        n=m/10; T=2*L/(n*c); dt=T/Nt; T=T-dt;
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        print("Progressive-cos-10xn="+zfi(m))
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        animation("Onde-Pression-sinus-10xn="+zfi(m)) 
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1
# -*- coding: utf-8 -*-
2
"""
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Debit son pulse
4
O. Thual, 21/08/2021
5
"""
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7
#  clear all
8
for iglob in list(globals().keys()):
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    if(iglob[0] != '_'):
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        exec('del {}'.format(iglob))
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# import libraries
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import numpy as np
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import matplotlib.pyplot as plt
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import os
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def inifig(xaxe=0,yaxe=0,xlab='x',ylab='y'):
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    plt.figure(2)
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    plt.axvline(xaxe)
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    plt.axhline(yaxe)
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    plt.xticks(fontsize=12)
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    plt.yticks(fontsize=12)
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    plt.xlabel(xlab,fontsize=16 )
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    plt.ylabel(ylab,fontsize=16)
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def zfi(x,le=2):
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    miss=le-len(str(x))
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    a='0'*miss+str(x)
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    return a
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def animationboth(name):
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    a=np.linspace(0,L,N+1);
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    acont=np.linspace(0,L,501);
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    t=0; 
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    dt=T/Nt
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    for i in range(0,Nt+1):
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        title=name+" i="+zfi(i)
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        titlefig=name
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        print(title)
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        fig=plt.figure(N,figsize=(7,4))
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        plt.xlabel('x',fontsize=16 )
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        plt.ylabel(r'$p$',fontsize=16)
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        plt.title(titlefig,fontsize=16)
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        t=dt*i;
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        # discret
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        xi=depla(a,t)
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        for dup in duprange:
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            plt.scatter(a+sc*xi,dup+0*xi,marker='o',color='blue',s=40)
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            amid=a[int(N/4)]; ximid=xi[int(N/4)];
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            plt.scatter(amid+sc*ximid,dup+0*ximid,marker='o',color='red',s=80)
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            amid=a[int(3*N/4)]; ximid=xi[int(3*N/4)];
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            plt.scatter(amid+sc*ximid,dup+0*ximid,marker='o',color='green',s=80)
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           #plt.scatter(a,dup+0*xi,marker='o',color='red',s=20)
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        # continu 
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        xicont=depla(acont,t)
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        pcont=signal(acont,t)
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        pleft=signalleft(acont,t)
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        pright=signalright(acont,t)
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        #plt.plot(acont,xicont,color='blue',linewidth=3)
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        plt.plot(acont+sc*xicont,pcont,color='black',linewidth=3)
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        plt.plot(acont+sc*xicont,pleft,color='green',linewidth=3)
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        plt.plot(acont+sc*xicont,pright,color='red',linewidth=3)
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        plt.xlim(0,L)
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        plt.ylim(ymin,ymax)
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        namei=name+zfi(i)+'.png';
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        plt.grid(color='black', axis='y', linestyle='-', linewidth=1)        
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        plt.grid(color='black', axis='x', linestyle='-', linewidth=1)        
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        plt.savefig(namei)
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        plt.show()
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        plt.close()
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    gifanim="Anim"+name+".gif"
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    #os.system('/opt/local/bin/convert -set delay '+delay+' '+name+'* '+gifanim);
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    os.system('/usr/local/bin/convert -set delay '+delay+' '+name+'* '+gifanim);
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    if flagp: os.system('rm '+name+'*');  
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# Main 
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F=False; T=True
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flagp=T; flagall=F;
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def pulse(a,d):
84
    al=0*a[a<-d]; ac=a[np.abs(a)<=d]; ar=0*a[a>d];
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    k=np.pi/d; fc=.5*(1+np.cos(k*ac));
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    f=np.concatenate((al,fc,ar))
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    return f
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def pulsem(a,d):
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    al=0*a[a<-d]; ac=a[np.abs(a)<=d]; ar=0*a[a>d];
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    k=np.pi/d; fc=ac-np.pi/k+np.sin(k*ac)/k
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    f=np.concatenate((al-2*np.pi/k,fc,ar))
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    return f
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def pulsep(a,d):
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    al=0*a[a<-d]; ac=a[np.abs(a)<=d]; ar=0*a[a>d];
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    k=np.pi/d; fc=ac+np.pi/k+np.sin(k*ac)/k
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    f=np.concatenate((al,fc,ar+2*np.pi/k))
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    return f
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# Deux pulses inegaux
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if T or flagall: 
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    N=30; L=10; d=2; c=1; 
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    T=(L+2*d)/c; Nt=20; sc=.5*L/N # scaling 
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    k=np.pi/d;
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    Al=.4; Ar=.6
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    #Al=0; Ar=.3; d=1
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    ymin=-.1; ymax=1;
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    #ymin=-2; ymax=2;
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    duprange=np.linspace(-.2,1,7)
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    delay="80"
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    # signal 
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    def depla(a,t):
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        xi=-Ar*pulsem(a+d-c*t,d)-Al*pulsep(a-L-d+c*t,d)
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        return xi
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    def signal(a,t):
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        am=a-c*t;ap=a+c*t;
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        p=Ar*pulse(a+d-c*t,d)+Al*pulse(a-L-d+c*t,d)
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        return p
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    def signalleft(a,t):
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        p=Al*pulse(a-L-d+c*t,d)
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        return p
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    def signalright(a,t):
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        p=Ar*pulse(a+d-c*t,d)
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        return p
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    animationboth("Deux-pulses-inegaux") 
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1
# -*- coding: utf-8 -*-
2
"""
3
Reflexion Transmission
4
O. Thual, 21/08/2021
5
"""
6
7
#  clear all
8
for iglob in list(globals().keys()):
9
    if(iglob[0] != '_'):
10
        exec('del {}'.format(iglob))
11
# import libraries
12
import numpy as np
13
import matplotlib.pyplot as plt
14
import os
15
16
17
def inifig(xaxe=0,yaxe=0,xlab='x',ylab='y'):
18
    plt.figure(2)
19
    plt.axvline(xaxe)
20
    plt.axhline(yaxe)
21
    plt.xticks(fontsize=12)
22
    plt.yticks(fontsize=12)
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    plt.xlabel(xlab,fontsize=16 )
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    plt.ylabel(ylab,fontsize=16)
25
    
26
def zfi(x,le=2):
27
    miss=le-len(str(x))
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    a='0'*miss+str(x)
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    return a
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def animatrois(name):
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    N=20; a=np.linspace(-L,L,N+1);
34
    acont=np.linspace(-L,L,501);
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    t=0; 
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    dt=Time/Nt
37
    for i in range(0,Nt+1):
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        title=name+" i="+zfi(i)
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        titlefig=name
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        print(title)
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        fig=plt.figure(i,figsize=(7,4))
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        plt.xlabel(r'$x$',fontsize=16 )
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        plt.ylabel(r'$f$',fontsize=16)
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        plt.title(titlefig,fontsize=16)
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        # signal
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        t=dt*i;
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        fin=finc(acont,t)
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        fre=fref(acont,t)
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        ftr=ftra(acont,t)
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        ftot=fin+fre+ftr
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        plt.plot(acont,fin,color='red',linewidth=3)
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        plt.plot(acont,fre,color='green',linewidth=3)
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        plt.plot(acont,ftr,color='red',linewidth=3)
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        plt.plot(acont,ftot,color='black',linewidth=3)
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        plt.plot([0,0],[ymin,ymax],color='blue',linewidth=3)
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        plt.xlim(-L,L2)
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        plt.ylim(ymin,ymax)
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        namei=name+zfi(i)+'.png';
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        plt.grid(color='black', axis='y', linestyle='-', linewidth=1)        
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        plt.savefig(namei)
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        plt.show()
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        plt.close()
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    gifanim="Anim"+name+".gif"
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    #os.system('/opt/local/bin/convert -set delay '+delay+' '+name+'* '+gifanim);
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    os.system('/usr/local/bin/convert -set delay '+delay+' '+name+'* '+gifanim);
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    if flagp: os.system('rm '+name+'*');  
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# Main 
70
F=False; T=True
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flagp=F; flagall=F;
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def pulse(a,d):
74
    al=0*a[a<-d]; ac=a[np.abs(a)<=d]; ar=0*a[a>d];
75
    k=np.pi/d; fc=.5*(1+np.cos(k*ac));
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    f=np.concatenate((al,fc,ar))
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    return f
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def leftsin(a,k):
81
    al=a[a<=0]; ar=0*a[a>0];
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    fl=-np.sin(k*al);
83
    f=np.concatenate((fl,ar))
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    return f
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def rightsin(a,k):
87
    al=0*a[a<=0]; ar=a[a>0];
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    fr=np.sin(k*ar);
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    f=np.concatenate((al,fr))
90
    return f
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# Reflexion Transmission harmonique
94
if T or flagall:
95
    L=10; d=5; A=1; rho=1; c1=1;c2=1;
96
    Re=.8; ymin=-2; ymax=2;
97
    Re=-.8; ymin=-2; ymax=2;
98
    Re=.5; ymin=-1.5; ymax=1.5;
99
    Re=1; ymin=-2; ymax=2;
100
    Re=-1; ymin=-2; ymax=2;
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    Tr=1-Re;
102
    print("c1=",c1,"c2=",c2,"Re=",Re)
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    k=np.pi/d; k2=c2/c1*k; L2=min(L,L*c2/c1);
104
    Time=4*L/c1; Nt=40;
105
    delay="40"
106
    
107
    # signal 
108
    def finc(a,t):
109
        al=a[a<=0]; ar=0*a[a>0];
110
        fl=leftsin(L+al-c1*t,k)
111
        f=np.concatenate((fl,ar))
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        return f
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    def fref(a,t):
114
        al=a[a<=0]; ar=0*a[a>0];
115
        fl=-Re*rightsin(-L+al+c1*t,k)
116
        f=np.concatenate((fl,ar))
117
        return f
118
    def ftra(a,t):
119
        al=0*a[a<=0]; ar=a[a>0];
120
        fr=Tr*leftsin(L+c1/c2*(ar-c2*t),k)
121
        f=np.concatenate((al,fr))
122
        return f
123
    
124
    animatrois("Reflexion-Transmission-Harm-R="+zfi(Re)) 
125
    print("c1=",c1,"c2=",c2)
126
    print("Re=",Re,"Tr=",Tr)
127
128
# Reflexion Transmission pulse
129
if F or flagall:
130
    L=10; d=5; A=1; rho=1; c1=1; c2=1; d=5; 
131
    Re=.8; ymin=-1; ymax=1;
132
    Re=-.8; ymin=-.2; ymax=2;
133
    #Re=.5; ymin=-.5; ymax=1;
134
    Tr=1-Re;
135
    print("c1=",c1,"c2=",c2,"Re=",Re)
136
    L2=min(L,L*c2/c1);
137
    Time=3*L/c1; Nt=40;
138
    delay="40"
139
   
140
    # signal 
141
    def finc(a,t):
142
        al=a[a<=0]; ar=0*a[a>0];
143
        fl=pulse(L+d+al-c1*t,d)
144
        f=np.concatenate((fl,ar))
145
        return f
146
    def fref(a,t):
147
        al=a[a<=0]; ar=0*a[a>0];
148
        fl=-Re*pulse(-L-d+al+c1*t,d)
149
        f=np.concatenate((fl,ar))
150
        return f
151
    def ftra(a,t):
152
        al=0*a[a<=0]; ar=a[a>0];
153
        fr=Tr*pulse(L+d+c1/c2*(ar-c2*t),d)
154
        f=np.concatenate((al,fr))
155
        return f
156
157
    animatrois("Reflexion-Transmission-Pulse-R="+zfi(Re))
158
    print("c1=",c1,"c2=",c2)
159
    print("Re=",Re,"Tr=",Tr)
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