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