Equations f(x 1 )= 2*sin(1*x)

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Equations f(x 1 )= 2*sin(1*x). Parameters: Amp freq 2 1. Equations f(x 1 )= 2*sin(1*x) f(x 2 )= -1*sin(2*x). Parameters: Amp freq 2 1 -1 2. Equations f(x 1 )= 2*sin(1*x) f(x 2 )= -1*sin(2*x) f(x 3 )= .67*sin(3*x). Parameters: Amp freq 2 1 -1 2 0.67 3. Equations
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Equationsf(x1)= 2*sin(1*x)Parameters:Amp freq 2 1Equationsf(x1)= 2*sin(1*x)f(x2)= -1*sin(2*x)Parameters:Amp freq 2 1-1 2Equationsf(x1)= 2*sin(1*x)f(x2)= -1*sin(2*x)f(x3)= .67*sin(3*x)Parameters:Amp freq 2 1-1 2 0.67 3Equationsf(x1)= 2*sin(1*x)f(x2)= -1*sin(2*x)f(x3)= .67*sin(3*x)f(x4)= -.5*sin(4*x)Parameters:Amp freq 2 1-1 2 0.67 3-0.5 4Equationsf(x1)= 2*sin(1*x)f(x2)= -1*sin(2*x)f(x3)= .67*sin(3*x)f(x4)= -.5*sin(4*x)f(x5)= .4*sin(5*x)Parameters:Amp freq 2 1-1 2 0.67 3-0.5 4 0.4 5Sum the first five termsEquationsf(x1)= 2*sin(1*x)f(x2)= -1*sin(2*x)f(x3)= .67*sin(3*x)f(x4)= -.5*sin(4*x)f(x5)= .4*sin(5*x)Parameters:Amp freq 2 1-1 2 0.67 3-0.5 4 0.4 5watch the magenta line as we sum the first ten termsSum the first ten termsGiven f(xi) = Amp * sin (freq * x)The List of parameters contains the same information as the magenta lineEquationsf(x1)= 2*sin(1*x)f(x2)= -1*sin(2*x)f(x3)= .67*sin(3*x)f(x4)= -.5*sin(4*x)f(x5)= .4*sin(5*x)f(x6)= -.33*sin(6*x)f(x7)= .29*sin(7*x)f(x8)= -.25*sin(8*x)f(x9)= .22*sin(9*x)f(x10)= -.2*sin(10*x) …Parameters:Amp freq 2 1-1 2 0.67 3-0.5 4 0.4 5-0.33 6 0.29 7-0.25 8 0.22 9 -0.2 10It is much easier to list the parameters then graph the sum of the functionsSum the first ten termsGiven f(xi) = A*sin(f*x)The list of parameters contains the same information as the magenta lineParameters:Amp freq 2 1-1 2 0.67 3-0.5 4 0.4 5-0.33 6 0.29 7-0.25 8 0.22 9 -0.2 10=It is much easier to list the parameters then graph the sum of the functionsThe first ten terms of f(xi) = A*sin(f *x) in Parameter SpaceParameters:Amp freq 2 1-1 2 0.67 3-0.5 4 0.4 5-0.33 6 0.29 7-0.25 8 0.22 9 -0.2 10Amplitude versus Frequency(aka amplitude spectrum)Amplitude versus Distance=Space DomainFrequency Domain (1/distance )
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