+ i:'RtR.t^RIHt^RIHt^RIHtHt^RI H t H t H t ^RI Ht^RIHtHt^RIHtHt^R IHt^R IHt^R IHtHtHt^R IHtHtH t ]PB!]] , 4t"!R R]4t#R#)zb This module has all the classes and functions related to waves in optics. **Contains** * TWave TWave)Basic)Expr) DerivativeFunction)NumberpiI)S)Symbolsymbols)_sympifysympify)exp)sqrt)atan2cossin)speed_of_lightmetersecondc2a]tRt^toRtR]P R]!R43Rlt] R4t ] R4t ] R4t ] R4t ] R 4t] R 4t] R 4t] R 4t] R 4tRt]tRtRtRtRtRtRtRtRtRtRtRtRt Vt!R#)rax This is a simple transverse sine wave travelling in a one-dimensional space. Basic properties are required at the time of creation of the object, but they can be changed later with respective methods provided. Explanation =========== It is represented as :math:`A \times cos(k*x - \omega \times t + \phi )`, where :math:`A` is the amplitude, :math:`\omega` is the angular frequency, :math:`k` is the wavenumber (spatial frequency), :math:`x` is a spatial variable to represent the position on the dimension on which the wave propagates, and :math:`\phi` is the phase angle of the wave. Arguments ========= amplitude : Sympifyable Amplitude of the wave. frequency : Sympifyable Frequency of the wave. phase : Sympifyable Phase angle of the wave. time_period : Sympifyable Time period of the wave. n : Sympifyable Refractive index of the medium. Raises ======= ValueError : When neither frequency nor time period is provided or they are not consistent. TypeError : When anything other than TWave objects is added. Examples ======== >>> from sympy import symbols >>> from sympy.physics.optics import TWave >>> A1, phi1, A2, phi2, f = symbols('A1, phi1, A2, phi2, f') >>> w1 = TWave(A1, f, phi1) >>> w2 = TWave(A2, f, phi2) >>> w3 = w1 + w2 # Superposition of two waves >>> w3 TWave(sqrt(A1**2 + 2*A1*A2*cos(phi1 - phi2) + A2**2), f, atan2(A1*sin(phi1) + A2*sin(phi2), A1*cos(phi1) + A2*cos(phi2)), 1/f, n) >>> w3.amplitude sqrt(A1**2 + 2*A1*A2*cos(phi1 - phi2) + A2**2) >>> w3.phase atan2(A1*sin(phi1) + A2*sin(phi2), A1*cos(phi1) + A2*cos(phi2)) >>> w3.speed 299792458*meter/(second*n) >>> w3.angular_velocity 2*pi*f NncVe#\V4p\PV, pVeN\V4p\PV, pVe(V\PV, 8wd \R4hVfVf \R4hVfXpVfXp\V4p\V4p\ V4p\ P !WW#WE4pV#)Nz/frequency and time_period should be consistent.z*Either frequency or time period is needed.)r r One ValueErrorrr__new__) cls amplitude frequencyphase time_periodr _frequency _time_periodobjs &&&&&& z/Users/tonyclaw/.openclaw/workspace/skills/math-calculator/venv/lib/python3.14/site-packages/sympy/physics/optics/waves.pyr TWave.__new__Ys  "";/K{*J   +I55?L&k 11$%VWW  !4IJ J  "I  &KY'  AJmmCIkM c (VP^,#)z Returns the amplitude of the wave. Examples ======== >>> from sympy import symbols >>> from sympy.physics.optics import TWave >>> A, phi, f = symbols('A, phi, f') >>> w = TWave(A, f, phi) >>> w.amplitude A argsselfs&r%rTWave.amplitudevsyy|r'c (VP^,#)z Returns the frequency of the wave, in cycles per second. Examples ======== >>> from sympy import symbols >>> from sympy.physics.optics import TWave >>> A, phi, f = symbols('A, phi, f') >>> w = TWave(A, f, phi) >>> w.frequency f r)r+s&r%rTWave.frequency yy|r'c (VP^,#)z Returns the phase angle of the wave, in radians. Examples ======== >>> from sympy import symbols >>> from sympy.physics.optics import TWave >>> A, phi, f = symbols('A, phi, f') >>> w = TWave(A, f, phi) >>> w.phase phi r)r+s&r%r TWave.phaser0r'c (VP^,#)z Returns the temporal period of the wave, in seconds per cycle. Examples ======== >>> from sympy import symbols >>> from sympy.physics.optics import TWave >>> A, phi, f = symbols('A, phi, f') >>> w = TWave(A, f, phi) >>> w.time_period 1/f r)r+s&r%r!TWave.time_periodr0r'c (VP^,#)z, Returns the refractive index of the medium r)r+s&r%rTWave.ns yy|r'c R\VPVP,, #)a: Returns the wavelength (spatial period) of the wave, in meters per cycle. It depends on the medium of the wave. Examples ======== >>> from sympy import symbols >>> from sympy.physics.optics import TWave >>> A, phi, f = symbols('A, phi, f') >>> w = TWave(A, f, phi) >>> w.wavelength 299792458*meter/(second*f*n) )crrr+s&r% wavelengthTWave.wavelengths"$..'((r'c <VPVP,#)a/ Returns the propagation speed of the wave, in meters per second. It is dependent on the propagation medium. Examples ======== >>> from sympy import symbols >>> from sympy.physics.optics import TWave >>> A, phi, f = symbols('A, phi, f') >>> w = TWave(A, f, phi) >>> w.speed 299792458*meter/(second*n) )r9rr+s&r%speed TWave.speeds"t~~--r'c >^\,VP,#)z Returns the angular velocity of the wave, in radians per second. Examples ======== >>> from sympy import symbols >>> from sympy.physics.optics import TWave >>> A, phi, f = symbols('A, phi, f') >>> w = TWave(A, f, phi) >>> w.angular_velocity 2*pi*f )rrr+s&r%angular_velocityTWave.angular_velocitys tDNN""r'c >^\,VP, #)a Returns the wavenumber of the wave, in radians per meter. Examples ======== >>> from sympy import symbols >>> from sympy.physics.optics import TWave >>> A, phi, f = symbols('A, phi, f') >>> w = TWave(A, f, phi) >>> w.wavenumber pi*second*f*n/(149896229*meter) )rr9r+s&r% wavenumberTWave.wavenumbers tDOO##r'c f^RIHp\V4PV!VP4,#)z!String representation of a TWave.)sstr)sympy.printingrEtype__name__r*)r,rEs& r%__str__ TWave.__str__s"'Dz""T$))_44r'c  \V\4'EdVPVP8XEdbVPVP8XEdF\\ VP ^,VP ^,,^VP ,VP ,\ VPVP, 4,,4VP\VP \VP4,VP \VP4,,VP \ VP4,VP \ VP4,,44#\R4h\\V4PR,4h)zw Addition of two waves will result in their superposition. The type of interference will depend on their phase angles. zJInterference of waves with different frequencies has not been implemented.z# and TWave objects cannot be added.) isinstancerrr9rrrr rrNotImplementedError TypeErrorrGrHr,others&&r%__add__ TWave.__add__sD eU # #~~0T__HXHX5XT$..!"3eooq6H"H1"&..L116LAAD&*jj5;;&>B@L@#@A"^^"4>>#djj/#A$s5;;/??$@!^^C O;$s5;;/??@A *+122DK003XXY Yr'c \V4p\V\4'd0\VPV,.VP R,O5!#\ \V4PR,4h)zD Multiplying a wave by a scalar rescales the amplitude of the wave. :NNz( and TWave objects cannot be multiplied.) rrLrrrr*rNrGrHrOs&&r%__mul__ TWave.__mul__,sV eV $ $-> " > >DK003]]^ ^r'c2VPRV,4#rTrQrOs&&r%__sub__ TWave.__sub__6s||BuH%%r'c$VPR4#rXrUr+s&r%__neg__ TWave.__neg__9s||Br'c$VPV4#NrZrOs&&r%__radd__TWave.__radd__<||E""r'c$VPV4#rbr^rOs&&r%__rmul__TWave.__rmul__?rer'c&V)PV4#rb)rcrOs&&r%__rsub__TWave.__rsub__Bs&&r'cVP\VP\R4,VP\R4,, VP ,\ ^, ,RR7,#)xtF)evaluate)rrrBr r?r rr,r*kwargss&*,r%_eval_rewrite_as_sinTWave._eval_rewrite_as_sinEs_~~c$//&+"=##F3K/#026**#=?A!t#DNSUU Ur'cVP\VP\R4,VP\R4,, VP ,4,#rmrn)rrrBr r?r rps&*,r%_eval_rewrite_as_cosTWave._eval_rewrite_as_cosIsL~~c$//&+"=##F3K/#026**#=>> >r'c\R4wr4rV\R4p\V!WV4V^4W4,\V!WV4V^4,,#)zmu, epsilon, x, tE)r rr)r,r*rqmuepsilonrmrnrys&*, r%_eval_rewrite_as_pdeTWave._eval_rewrite_as_pdeMsG#$78Q SM!A'1a(2:j1!Q6O+OOOr'c VP\\VP\ R4,VP \ R4,, VP ,,4,#ru)rrr rBr r?r rps&*,r%_eval_rewrite_as_expTWave._eval_rewrite_as_expRsS~~c!T__VC[%@##F3K/&026**&=#>?? ?r')"rH __module__ __qualname____firstlineno____doc__r Zeror rpropertyrrr r!rr9r<r?rBrI__repr__rQrUr[r_rcrgrjrrrvr|r__static_attributes____classdictcell__) __classdict__s@r%rrs&:~&&Sk : """ ))&..$##"$$"5 HZ,_& ##'U>P ??r'N)$r__all__sympy.core.basicrsympy.core.exprrsympy.core.functionrrsympy.core.numbersrrr sympy.core.singletonr sympy.core.symbolr r sympy.core.sympifyr r&sympy.functions.elementary.exponentialr(sympy.functions.elementary.miscellaneousr(sympy.functions.elementary.trigonometricrrrsympy.physics.unitsrrr convert_tor8rrr'r%rsa )" 4.."/069FF==eFl+y?Dy?r'