o 8Vag%@sdZdgZddlmZmZmZmZmZmZm Z m Z m Z m Z m Z ddlmZddlmZmZmZeeeZGdddeZdS)zb This module has all the classes and functions related to waves in optics. **Contains** * TWave TWave) sympifypisincossqrtNumberSymbolSsymbols Derivativeatan2)Expr)speed_of_lightmetersecondc@seZdZdZdejdedfddZeddZ edd Z ed d Z ed d Z eddZ eddZeddZeddZddZeZddZddZddZddZd d!Zd"d#Zd$d%Zd&d'Zd(d)Zd*d+Zd,d-ZdS).ra, 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))) >>> 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 NncCst|}t|}t|}t|}t|}||_||_||_||_||_|dur-d|j|_|durEd|j|_|durE|d|krEtd|durQ|durStddSdS)Nz/frequency and time_period should be consistent.z*Either frequency or time period is needed.)r _frequency _amplitude_phase _time_period_n ValueError)self amplitude frequencyphase time_periodrr>> 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 )rrrrr rmzTWave.frequencycCr")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 )rr#rrr rr$zTWave.time_periodcCst|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#rrr wavelengthszTWave.wavelengthcCr")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 )rr#rrr rszTWave.amplitudecCr")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 )rr#rrr rr$z TWave.phasecCs |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#rrr speeds z 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 )rrr#rrr angular_velocityzTWave.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#rrr wavenumberr*zTWave.wavenumbercCs ddlm}t|j||jS)z!String representation of a TWave.r)sstr)Zsympy.printingr,type__name__args)rr,rrr __str__s z TWave.__str__c Cst|trU|j|jkrQ|j|jkrQtt|jd|jdd|j|jt|j|j|jt |jt |j|jt |j|jt|j|jt|jSt dt t |jd)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 can't be added.) isinstancerrr&rrrrrr rNotImplementedError TypeErrorr-r.rotherrrr __add__s,   z TWave.__add__cCsDt|}t|trt|j|g|jddRStt|jd)zT Multiplying a wave by a scalar rescales the amplitude of the wave. rNz' and TWave objects can't be multiplied.) rr1rrrr/r3r-r.r4rrr __mul__s  z TWave.__mul__cCs|d|SNr6r4rrr __sub__%sz TWave.__sub__cCs |dSr8r7r#rrr __neg__( z TWave.__neg__cC ||SNr:r4rrr __radd__+r>zTWave.__radd__cCr?r@r<r4rrr __rmul__.r>zTWave.__rmul__cCs | |Sr@)rAr4rrr __rsub__1s zTWave.__rsub__cOs8|jt|jtd|jtd|jtdddS)Nxtr(F)Zevaluate)rrr+r r)rrrr/kwargsrrr _eval_rewrite_as_sin4s zTWave._eval_rewrite_as_sincOs,|jt|jtd|jtd|jS)NrDrE)rrr+r r)rrFrrr _eval_rewrite_as_cos8s  zTWave._eval_rewrite_as_cosc OsPddlm}td\}}}}|d}t||||d||t||||dS)Nr)Functionzmu, epsilon, x, tEr()sympyrJr r ) rr/rGrJZmuepsilonrDrErKrrr _eval_rewrite_as_pde<s ,zTWave._eval_rewrite_as_pdecOs@ddlm}m}|j|||jtd|jtd|jS)Nr)expIrDrE)rLrOrPrr+r r)r)rr/rGrOrPrrr _eval_rewrite_as_expBs   zTWave._eval_rewrite_as_exp)r. __module__ __qualname____doc__r ZZeror r!propertyrrr&rrr'r)r+r0__repr__r6r7r;r=rArBrCrHrIrNrQrrrr rsH?           N)rT__all__rLrrrrrrr r r r r Zsympy.core.exprrZsympy.physics.unitsrrrZ convert_tor%rrrrr s4