U Zʹj:'@sdZdgZddlmZddlmZddlmZmZddl m Z m Z m Z ddl mZddlmZmZdd lmZmZdd lmZdd lmZdd lmZmZmZdd lmZmZm Z e!ee Z"GdddeZ#dS)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@seZdZdZdejdedfddZeddZ edd Z ed d Z ed d Z eddZ eddZeddZeddZeddZddZeZddZddZddZd d!Zd"d#Zd$d%Zd&d'Zd(d)Zd*d+Zd,d-Zd.d/ZdS)0ra4 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 Cs|dk rt|}tj|}|dk rRt|}tj|}|dk rR|tj|krRtd|dkrj|dkrjtd|dkrv|}|dkr|}t|}t|}t|}t||||||}|S)Nz/frequency and time_period should be consistent.z*Either frequency or time period is needed.)r r ZOne ValueErrorrr__new__) cls amplitude frequencyphase time_periodrZ _frequencyZ _time_periodobjr Y/var/www/html/bwave/python/venv/lib/python3.8/site-packages/sympy/physics/optics/waves.pyrYs(  z TWave.__new__cCs |jdS)a! 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 rargsselfr r r!rvszTWave.amplitudecCs |jdS)a? 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$r r r!rszTWave.frequencycCs |jdS)a5 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$r r r!rsz TWave.phasecCs |jdS)aI Returns the temporal period of the wave, in seconds per cycle. Examples ======== >>> from sympy import symbols >>> from sympy.physics.optics import TWave >>> A, phi, f = symbols('A, phi, f') >>> w = TWave(A, f, phi) >>> w.time_period 1/f r"r$r r r!rszTWave.time_periodcCs |jdS)z< Returns the refractive index of the medium r"r$r r r!rszTWave.ncCst|j|jS)a Returns the wavelength (spatial period) of the wave, in meters per cycle. It depends on the medium of the wave. Examples ======== >>> from sympy import symbols >>> from sympy.physics.optics import TWave >>> A, phi, f = symbols('A, phi, f') >>> w = TWave(A, f, phi) >>> w.wavelength 299792458*meter/(second*f*n) )crrr$r r r! wavelengthszTWave.wavelengthcCs |j|jS)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+rr$r r r!speedsz TWave.speedcCsdt|jS)aS Returns the angular velocity of the wave, in radians per second. Examples ======== >>> from sympy import symbols >>> from sympy.physics.optics import TWave >>> A, phi, f = symbols('A, phi, f') >>> w = TWave(A, f, phi) >>> w.angular_velocity 2*pi*f r')rrr$r r r!angular_velocityszTWave.angular_velocitycCsdt|jS)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) r')rr+r$r r r! wavenumberszTWave.wavenumbercCs ddlm}t|j||jS)z!String representation of a TWave.r)sstr)Zsympy.printingr/type__name__r#)r%r/r r r!__str__s z TWave.__str__c Cst|tr|j|jkr|j|jkrtt|jd|jdd|j|jt|j|j|jt|jt |j|jt |j|jt|j|jt|jSt dnt t |j ddS)z Addition of two waves will result in their superposition. The type of interference will depend on their phase angles. r'zJInterference of waves with different frequencies has not been implemented.z# and TWave objects cannot be added.N) isinstancerrr+rrrrrrNotImplementedError TypeErrorr0r1r%otherr r r!__add__s,   z TWave.__add__cCsFt|}t|tr0t|j|f|jddStt|jddS)zT Multiplying a wave by a scalar rescales the amplitude of the wave. r&Nz( and TWave objects cannot be multiplied.) rr3rrrr#r5r0r1r6r r r!__mul__,s z TWave.__mul__cCs|d|SNr8r6r r r!__sub__6sz TWave.__sub__cCs |dSr:r9r$r r r!__neg__9sz TWave.__neg__cCs ||SNr<r6r r r!__radd__<szTWave.__radd__cCs ||Sr@r>r6r r r!__rmul__?szTWave.__rmul__cCs | |Sr@)rAr6r r r!__rsub__BszTWave.__rsub__cOs8|jt|jtd|jtd|jtdddS)Nxtr'F)evaluate)rrr.r r-rrr%r#kwargsr r r!_eval_rewrite_as_sinEs zTWave._eval_rewrite_as_sincOs,|jt|jtd|jtd|jSNrDrE)rrr.r r-rrGr r r!_eval_rewrite_as_cosIs  zTWave._eval_rewrite_as_coscOsDtd\}}}}td}t||||d||t||||dS)Nzmu, epsilon, x, tEr')r rr)r%r#rHmuepsilonrDrErLr r r!_eval_rewrite_as_pdeMszTWave._eval_rewrite_as_pdecOs0|jtt|jtd|jtd|jSrJ)rrr r.r r-rrGr r r!_eval_rewrite_as_expRs  zTWave._eval_rewrite_as_exp)r1 __module__ __qualname____doc__r ZZeror rpropertyrrrrrr+r,r-r.r2__repr__r8r9r=r?rArBrCrIrKrOrPr r r r!rsJ?           N)$rS__all__Zsympy.core.basicrZsympy.core.exprrZsympy.core.functionrrZsympy.core.numbersrrr Zsympy.core.singletonr Zsympy.core.symbolr r Zsympy.core.sympifyr rZ&sympy.functions.elementary.exponentialrZ(sympy.functions.elementary.miscellaneousrZ(sympy.functions.elementary.trigonometricrrrZsympy.physics.unitsrrrZ convert_tor*rr r r r!s