def test_twave():
A1, phi1, A2, phi2, f = symbols('A1, phi1, A2, phi2, f')
n = Symbol('n') # Refractive index
t = Symbol('t') # Time
x = Symbol('x') # Spatial varaible
k = Symbol('k') # Wave number
E = Function('E')
exp = C.exp
w1 = TWave(A1, f, phi1)
w2 = TWave(A2, f, phi2)
assert w1.amplitude == A1
assert w1.frequency == f
assert w1.phase == phi1
assert w1.wavelength == c/(f*n)
assert w1.time_period == 1/f
w3 = w1 + w2
assert w3.amplitude == sqrt(A1**2 + 2*A1*A2*cos(phi1 - phi2) + A2**2)
assert w3.frequency == f
assert w3.wavelength == c/(f*n)
assert w3.time_period == 1/f
assert w3.angular_velocity == 2*pi*f
assert w3.wavenumber == 2*pi*f*n/c
assert simplify(w3.rewrite('sin') - sqrt(A1**2 + 2*A1*A2*cos(phi1 - phi2)
+ A2**2)*sin(pi*f*n*x*s/(149896229*m) - 2*pi*f*t + phi1 + phi2 + pi/2)) == 0
assert w3.rewrite('pde') == epsilon*mu*Derivative(E(x, t), t, t) + Derivative(E(x, t), x, x)
assert w3.rewrite(cos) == sqrt(A1**2 + 2*A1*A2*cos(phi1 - phi2)
+ A2**2)*cos(pi*f*n*x*s/(149896229*m) - 2*pi*f*t + phi1 + phi2)
assert w3.rewrite('exp') == sqrt(A1**2 + 2*A1*A2*cos(phi1 - phi2)
+ A2**2)*exp(I*(pi*f*n*x*s/(149896229*m) - 2*pi*f*t + phi1 + phi2))
def test_twave():
A1, phi1, A2, phi2, f = symbols('A1, phi1, A2, phi2, f')
n = Symbol('n') # Refractive index
t = Symbol('t') # Time
x = Symbol('x') # Spatial variable
k = Symbol('k') # Wavenumber
E = Function('E')
w1 = TWave(A1, f, phi1)
w2 = TWave(A2, f, phi2)
assert w1.amplitude == A1
assert w1.frequency == f
assert w1.phase == phi1
assert w1.wavelength == c / (f * n)
assert w1.time_period == 1 / f
assert w1.angular_velocity == 2 * pi * f
assert w1.wavenumber == 2 * pi * f * n / c
assert w1.speed == c / n
w3 = w1 + w2
assert w3.amplitude == sqrt(A1**2 + 2 * A1 * A2 * cos(phi1 - phi2) + A2**2)
assert w3.frequency == f
assert w3.phase == atan2(A1 * cos(phi1) + A2 * cos(phi2),
A1 * sin(phi1) + A2 * sin(phi2))
assert w3.wavelength == c / (f * n)
assert w3.time_period == 1 / f
assert w3.angular_velocity == 2 * pi * f
assert w3.wavenumber == 2 * pi * f * n / c
assert w3.speed == c / n
assert simplify(
w3.rewrite(sin) -
sqrt(A1**2 + 2 * A1 * A2 * cos(phi1 - phi2) + A2**2) *
sin(pi * f * n * x * s / (149896229 * m) - 2 * pi * f * t +
atan2(A1 * cos(phi1) + A2 * cos(phi2),
A1 * sin(phi1) + A2 * sin(phi2)) + pi / 2)) == 0
assert w3.rewrite('pde') == epsilon * mu * Derivative(E(
x, t), t, t) + Derivative(E(x, t), x, x)
assert w3.rewrite(
cos) == sqrt(A1**2 + 2 * A1 * A2 * cos(phi1 - phi2) +
A2**2) * cos(pi * f * n * x * s /
(149896229 * m) - 2 * pi * f * t +
atan2(A1 * cos(phi1) + A2 * cos(phi2),
A1 * sin(phi1) + A2 * sin(phi2)))
assert w3.rewrite(
exp) == sqrt(A1**2 + 2 * A1 * A2 * cos(phi1 - phi2) + A2**2) * exp(
I * (pi * f * n * x * s / (149896229 * m) - 2 * pi * f * t +
atan2(A1 * cos(phi1) + A2 * cos(phi2),
A1 * sin(phi1) + A2 * sin(phi2))))
w4 = TWave(A1, None, 0, 1 / f)
assert w4.frequency == f
raises(ValueError, lambda: TWave(A1))
raises(ValueError, lambda: TWave(A1, f, phi1, t))
def test_twave():
A1, phi1, A2, phi2, f = symbols('A1, phi1, A2, phi2, f')
c = Symbol('c') # Speed of light in vacuum
n = Symbol('n') # Refractive index
t = Symbol('t') # Time
w1 = TWave(A1, f, phi1)
w2 = TWave(A2, f, phi2)
assert w1.amplitude == A1
assert w1.frequency == f
assert w1.phase == phi1
assert w1.wavelength == c / (f * n)
assert w1.time_period == 1 / f
w3 = w1 + w2
assert w3.amplitude == sqrt(A1**2 + 2 * A1 * A2 * cos(phi1 - phi2) + A2**2)
assert w3.frequency == f
assert w3.wavelength == c / (f * n)
assert w3.time_period == 1 / f
assert w3.angular_velocity == 2 * pi * f
assert w3.equation() == sqrt(A1**2 + 2 * A1 * A2 * cos(phi1 - phi2) +
A2**2) * cos(2 * pi * f * t + phi1 + phi2)