B ["@sdZddlmZmZdgZddlmZmZmZm Z m Z m Z m Z m Z mZmZddlmZddlmZmZmZeeeZGdddeZdS) zb This module has all the classes and functions related to waves in optics. **Contains** * TWave )print_functiondivisionTWave) sympifypisincossqrtSymbolSsymbols Derivativeatan2)Expr)speed_of_lightmetersecondc@seZdZdZdejdedfddZeddZ edd Z ed d Z ed d Z eddZ eddZeddZeddZddZeZddZddZddZddZd 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. 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 velocity, :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*cos(phi1) + A2*cos(phi2), A1*sin(phi1) + A2*sin(phi2))) >>> w3.amplitude sqrt(A1**2 + 2*A1*A2*cos(phi1 - phi2) + A2**2) >>> w3.phase atan2(A1*cos(phi1) + A2*cos(phi2), A1*sin(phi1) + A2*sin(phi2)) >>> w3.speed 299792458*meter/(second*n) >>> w3.angular_velocity 2*pi*f NncCst|}t|}t|}t|}t|}||_||_||_||_||_|dk rZd|j|_|dk rd|j|_|dk r|d|krtd|dkr|dkrtddS)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 9lib/python3.7/site-packages/sympy/physics/optics/waves.py__init__Qs&   zTWave.__init__cCs|jS)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)rr r r!rlszTWave.frequencycCs|jS)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)rr r r!r~szTWave.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) )crr)rr r r! wavelengthszTWave.wavelengthcCs|jS)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 )r)rr r r!rszTWave.amplitudecCs|jS)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)rr r r!rsz 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$r)rr r r!speedsz TWave.speedcCsdt|jS)aS Returns the angular velocity of the wave, in radians per second. Examples ======== >>> from sympy import symbols >>> from sympy.physics.optics import TWave >>> A, phi, f = symbols('A, phi, f') >>> w = TWave(A, f, phi) >>> w.angular_velocity 2*pi*f )rr)rr r r!angular_velocityszTWave.angular_velocitycCsdt|jS)a_ Returns the wavenumber of the wave, in radians per meter. Examples ======== >>> from sympy import symbols >>> from sympy.physics.optics import TWave >>> A, phi, f = symbols('A, phi, f') >>> w = TWave(A, f, phi) >>> w.wavenumber pi*second*f*n/(149896229*meter) r&)rr$)rr r r! wavenumberszTWave.wavenumbercCs ddlm}t|j||jS)z!String representation of a TWave.r)sstr)Zsympy.printingr)type__name__args)rr)r r r!__str__s z TWave.__str__c Cst|tr|j|jkr|j|jkrtt|jd|jdd|j|jt|j|j |j t |jt|j|jt|j|jt |j|jt |jSt dntt|jddS)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.N) isinstancerrr$r rrrrrrrrNotImplementedError TypeErrorr*r+)rotherr r r!__add__s  z TWave.__add__cGs8|jt|jtd|jtd|jtdddS)Nxtr&F)Zevaluate)rrr(r r'rr)rr,r r r!_eval_rewrite_as_sinszTWave._eval_rewrite_as_sincGs,|jt|jtd|jtd|jS)Nr3r4)rrr(r r'r)rr,r r r!_eval_rewrite_as_cosszTWave._eval_rewrite_as_coscGsPddlm}td\}}}}|d}t||||d||t||||dS)Nr)Functionzmu, epsilon, x, tEr&)sympyr7r r )rr,r7Zmuepsilonr3r4r8r r r!_eval_rewrite_as_pde"s zTWave._eval_rewrite_as_pdecGs@ddlm}m}|j|||jtd|jtd|jS)Nr)expIr3r4)r9r<r=rr(r r'r)rr,r<r=r r r!_eval_rewrite_as_exp(szTWave._eval_rewrite_as_exp)r+ __module__ __qualname____doc__r ZZeror r"propertyrrr$rrr%r'r(r-__repr__r2r5r6r;r>r r r r!rs(9        N)rAZ __future__rr__all__r9rrrrr r r r r rZsympy.core.exprrZsympy.physics.unitsrrrZ convert_tor#rr r r r!s0