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from sympy.core.function import (Derivative, Function) |
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from sympy.core.numbers import (I, pi) |
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from sympy.core.symbol import (Symbol, symbols) |
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from sympy.functions.elementary.miscellaneous import sqrt |
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from sympy.functions.elementary.trigonometric import (atan2, cos, sin) |
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from sympy.simplify.simplify import simplify |
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from sympy.abc import epsilon, mu |
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from sympy.functions.elementary.exponential import exp |
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from sympy.physics.units import speed_of_light, m, s |
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from sympy.physics.optics import TWave |
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from sympy.testing.pytest import raises |
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c = speed_of_light.convert_to(m/s) |
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def test_twave(): |
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A1, phi1, A2, phi2, f = symbols('A1, phi1, A2, phi2, f') |
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n = Symbol('n') |
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t = Symbol('t') |
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x = Symbol('x') |
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E = Function('E') |
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w1 = TWave(A1, f, phi1) |
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w2 = TWave(A2, f, phi2) |
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assert w1.amplitude == A1 |
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assert w1.frequency == f |
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assert w1.phase == phi1 |
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assert w1.wavelength == c/(f*n) |
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assert w1.time_period == 1/f |
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assert w1.angular_velocity == 2*pi*f |
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assert w1.wavenumber == 2*pi*f*n/c |
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assert w1.speed == c/n |
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w3 = w1 + w2 |
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assert w3.amplitude == sqrt(A1**2 + 2*A1*A2*cos(phi1 - phi2) + A2**2) |
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assert w3.frequency == f |
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assert w3.phase == atan2(A1*sin(phi1) + A2*sin(phi2), A1*cos(phi1) + A2*cos(phi2)) |
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assert w3.wavelength == c/(f*n) |
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assert w3.time_period == 1/f |
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assert w3.angular_velocity == 2*pi*f |
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assert w3.wavenumber == 2*pi*f*n/c |
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assert w3.speed == c/n |
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assert simplify(w3.rewrite(sin) - w2.rewrite(sin) - w1.rewrite(sin)) == 0 |
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assert w3.rewrite('pde') == epsilon*mu*Derivative(E(x, t), t, t) + Derivative(E(x, t), x, x) |
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assert w3.rewrite(cos) == sqrt(A1**2 + 2*A1*A2*cos(phi1 - phi2) |
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+ A2**2)*cos(pi*f*n*x*s/(149896229*m) - 2*pi*f*t + atan2(A1*sin(phi1) |
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+ A2*sin(phi2), A1*cos(phi1) + A2*cos(phi2))) |
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assert w3.rewrite(exp) == sqrt(A1**2 + 2*A1*A2*cos(phi1 - phi2) |
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+ A2**2)*exp(I*(-2*pi*f*t + atan2(A1*sin(phi1) + A2*sin(phi2), A1*cos(phi1) |
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+ A2*cos(phi2)) + pi*s*f*n*x/(149896229*m))) |
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w4 = TWave(A1, None, 0, 1/f) |
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assert w4.frequency == f |
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w5 = w1 - w2 |
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assert w5.amplitude == sqrt(A1**2 - 2*A1*A2*cos(phi1 - phi2) + A2**2) |
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assert w5.frequency == f |
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assert w5.phase == atan2(A1*sin(phi1) - A2*sin(phi2), A1*cos(phi1) - A2*cos(phi2)) |
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assert w5.wavelength == c/(f*n) |
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assert w5.time_period == 1/f |
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assert w5.angular_velocity == 2*pi*f |
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assert w5.wavenumber == 2*pi*f*n/c |
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assert w5.speed == c/n |
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assert simplify(w5.rewrite(sin) - w1.rewrite(sin) + w2.rewrite(sin)) == 0 |
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assert w5.rewrite('pde') == epsilon*mu*Derivative(E(x, t), t, t) + Derivative(E(x, t), x, x) |
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assert w5.rewrite(cos) == sqrt(A1**2 - 2*A1*A2*cos(phi1 - phi2) |
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+ A2**2)*cos(-2*pi*f*t + atan2(A1*sin(phi1) - A2*sin(phi2), A1*cos(phi1) |
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- A2*cos(phi2)) + pi*s*f*n*x/(149896229*m)) |
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assert w5.rewrite(exp) == sqrt(A1**2 - 2*A1*A2*cos(phi1 - phi2) |
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+ A2**2)*exp(I*(-2*pi*f*t + atan2(A1*sin(phi1) - A2*sin(phi2), A1*cos(phi1) |
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- A2*cos(phi2)) + pi*s*f*n*x/(149896229*m))) |
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w6 = 2*w1 |
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assert w6.amplitude == 2*A1 |
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assert w6.frequency == f |
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assert w6.phase == phi1 |
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w7 = -w6 |
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assert w7.amplitude == -2*A1 |
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assert w7.frequency == f |
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assert w7.phase == phi1 |
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raises(ValueError, lambda:TWave(A1)) |
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raises(ValueError, lambda:TWave(A1, f, phi1, t)) |
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