\h:'SrS/rSSKJr SSKJr SSKJrJr SSK J r J r J r SSK Jr SSKJrJr SS KJrJr SS KJr SS KJr SS KJrJrJr SS KJrJrJ r \RB"\\ - 5r""SS\5r#g)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_lightmetersecondc&\rSrSrSrS\R S\"S54Sjr\ S5r \ S5r \ S5r \ S 5r \ S 5r\ S 5r\ S 5r\ S 5r\ S5rSr\rSrSrSrSrSrSrSrSrSrSrSrSr g)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 Nnc|Ub[U5n[RU- nUbC[U5n[RU- nUb"U[RU- :wa [S5eUcUc [S5eUcWnUcWn[U5n[U5n[ U5n[ R "XX#XE5nU$)Nz/frequency and time_period should be consistent.z*Either frequency or time period is needed.)rr One ValueErrorrr__new__) cls amplitude frequencyphase time_periodr _frequency _time_periodobjs R/var/www/auris/envauris/lib/python3.13/site-packages/sympy/physics/optics/waves.pyr TWave.__new__Ys  "";/K{*J   +I55?L&k 11$%VWW  !4IJ J  "I  &KY'  AJmmCIkM c URS$)z Returns the amplitude of the wave. Examples ======== >>> from sympy import symbols >>> from sympy.physics.optics import TWave >>> A, phi, f = symbols('A, phi, f') >>> w = TWave(A, f, phi) >>> w.amplitude A rargsselfs r'r TWave.amplitudevsyy|r)c URS$)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'r!TWave.frequency yy|r)c URS$)z Returns the phase angle of the wave, in radians. Examples ======== >>> from sympy import symbols >>> from sympy.physics.optics import TWave >>> A, phi, f = symbols('A, phi, f') >>> w = TWave(A, f, phi) >>> w.phase phi r+r-s r'r" TWave.phaser3r)c URS$)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_periodr3r)c URS$)z, Returns the refractive index of the medium r+r-s r'rTWave.ns yy|r)cB[URUR-- $)a: Returns the wavelength (spatial period) of the wave, in meters per cycle. It depends on the medium of the wave. Examples ======== >>> from sympy import symbols >>> from sympy.physics.optics import TWave >>> A, phi, f = symbols('A, phi, f') >>> w = TWave(A, f, phi) >>> w.wavelength 299792458*meter/(second*f*n) )cr!rr-s r' wavelengthTWave.wavelengths"$..'((r)c4URUR-$)a/ Returns the propagation speed of the wave, in meters per second. It is dependent on the propagation medium. Examples ======== >>> from sympy import symbols >>> from sympy.physics.optics import TWave >>> A, phi, f = symbols('A, phi, f') >>> w = TWave(A, f, phi) >>> w.speed 299792458*meter/(second*n) )r?r!r-s r'speed TWave.speeds"t~~--r)c.S[-UR-$)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 r5)r r!r-s r'angular_velocityTWave.angular_velocitys tDNN""r)c.S[-UR- $)a Returns the wavenumber of the wave, in radians per meter. Examples ======== >>> from sympy import symbols >>> from sympy.physics.optics import TWave >>> A, phi, f = symbols('A, phi, f') >>> w = TWave(A, f, phi) >>> w.wavenumber pi*second*f*n/(149896229*meter) r5)r r?r-s r' wavenumberTWave.wavenumbers tDOO##r)c^SSKJn [U5RU"UR5-$)z!String representation of a TWave.r)sstr)sympy.printingrKtype__name__r,)r.rKs r'__str__ TWave.__str__s"'Dz""T$))_44r)c  [U[5(GaNURUR:XGa(URUR:XGa [[ UR S-UR S--SUR -UR -[ URUR- 5--5UR[UR [UR5-UR [UR5--UR [ UR5-UR [ UR5--55$[S5e[[U5RS-5e)zw Addition of two waves will result in their superposition. The type of interference will depend on their phase angles. r5zJInterference of waves with different frequencies has not been implemented.z# and TWave objects cannot be added.) isinstancerr!r?rr rr"rrNotImplementedError TypeErrorrMrNr.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[U5n[U[5(a&[URU-/UR SSQ76$[ [U5RS-5e)zD Multiplying a wave by a scalar rescales the amplitude of the wave. r1Nz( and TWave objects cannot be multiplied.) rrRrrr r,rTrMrNrUs r'__mul__ TWave.__mul__,sX eV $ $-> !" > >DK003]]^ ^r)c*URSU-5$NrWrUs r'__sub__ TWave.__sub__6s||BuH%%r)c$URS5$r]rZr-s r'__neg__ TWave.__neg__9s||Br)c$URU5$Nr_rUs r'__radd__TWave.__radd__<||E""r)c$URU5$rgrcrUs r'__rmul__TWave.__rmul__?rjr)c&U*RU5$rg)rhrUs r'__rsub__TWave.__rsub__Bs&&r)cUR[UR[S5-UR[S5-- UR -[ S- -SS9-$)Nxtr5F)evaluate)r rrHr rEr"r r.r,kwargss r'_eval_rewrite_as_sinTWave._eval_rewrite_as_sinEs_~~c$//&+"=##F3K/#026**#=?A!t#DNSUU Ur)cUR[UR[S5-UR[S5-- UR -5-$Nrrrs)r rrHr rEr"rus r'_eval_rewrite_as_cosTWave._eval_rewrite_as_cosIsL~~c$//&+"=##F3K/#026**#=>> >r)c[S5up4pV[S5n[U"XV5US5X4-[U"XV5US5--$)Nzmu, epsilon, x, tEr5)r rr)r.r,rvmuepsilonrrrsr~s r'_eval_rewrite_as_pdeTWave._eval_rewrite_as_pdeMsG#$78Q SM!A'1a(2:j1!Q6O+OOOr)c UR[[UR[ S5-UR [ S5-- UR --5-$rz)r rr rHr rEr"rus r'_eval_rewrite_as_expTWave._eval_rewrite_as_expRsS~~c!T__VC[%@##F3K/&026**&=#>?? ?r))!rN __module__ __qualname____firstlineno____doc__r Zeror rpropertyr r!r"r#rr?rBrErHrO__repr__rWrZr`rdrhrlrorwr{rr__static_attributes__rr)r'rrs:~&&Sk : """ ))&..$##"$$"5 HZ,_& ##'U>P ?r)N)$r__all__sympy.core.basicrsympy.core.exprrsympy.core.functionrrsympy.core.numbersrr r sympy.core.singletonr sympy.core.symbolr r sympy.core.sympifyrr&sympy.functions.elementary.exponentialr(sympy.functions.elementary.miscellaneousr(sympy.functions.elementary.trigonometricrrrsympy.physics.unitsrrr convert_tor>rrr)r'rsa )" 4.."/069FF==eFl+y?Dy?r)