o o h:'@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|dur t|}tj|}|dur)t|}tj|}|dur)|tj|kr)td|dur5|dur5td|dur;|}|durA|}t|}t|}t|}t||||||}|S)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_periodobjr#n/var/www/html/construction_image-detection-poc/venv/lib/python3.10/site-packages/sympy/physics/optics/waves.pyrYs(  z TWave.__new__cC |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$rvs zTWave.amplitudecCr%)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$r zTWave.frequencycCr%)a5 Returns the phase angle of the wave, in radians. Examples ======== >>> from sympy import symbols >>> from sympy.physics.optics import TWave >>> A, phi, f = symbols('A, phi, f') >>> w = TWave(A, f, phi) >>> w.phase phi r&r(r#r#r$rr+z TWave.phasecCr%)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$rr+zTWave.time_periodcCr%)z< Returns the refractive index of the medium r&r(r#r#r$rs zTWave.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) )r0rr(r#r#r$speeds z TWave.speedcCsdt|jS)aS Returns the angular velocity of the wave, in radians per second. Examples ======== >>> from sympy import symbols >>> from sympy.physics.optics import TWave >>> A, phi, f = symbols('A, phi, f') >>> w = TWave(A, f, phi) >>> w.angular_velocity 2*pi*f r,)rrr(r#r#r$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,)rr0r(r#r#r$ wavenumberr3zTWave.wavenumbercCs ddlm}t|j||jS)z!String representation of a TWave.r)sstr)sympy.printingr5type__name__r')r)r5r#r#r$__str__s z TWave.__str__c Cst|trU|j|jkrQ|j|jkrQtt|jd|jdd|j|jt|j|j|jt|jt |j|jt |j|jt|j|jt|jSt dt t |j d)z Addition of two waves will result in their superposition. The type of interference will depend on their phase angles. r,zJInterference of waves with different frequencies has not been implemented.z# and TWave objects cannot be added.) isinstancerrr0rrrrrrNotImplementedError TypeErrorr7r8r)otherr#r#r$__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. r*Nz( and TWave objects cannot be multiplied.) rr:rrrr'r<r7r8r=r#r#r$__mul__,s  z TWave.__mul__cCs|d|SNr?r=r#r#r$__sub__6sz TWave.__sub__cCs |dSrAr@r(r#r#r$__neg__9 z TWave.__neg__cC ||SNrCr=r#r#r$__radd__<rGzTWave.__radd__cCrHrIrEr=r#r#r$__rmul__?rGzTWave.__rmul__cCs | |SrI)rJr=r#r#r$__rsub__Bs zTWave.__rsub__cOs8|jt|jtd|jtd|jtdddS)Nxtr,F)evaluate)rrr4r r2rrr)r'kwargsr#r#r$_eval_rewrite_as_sinEs zTWave._eval_rewrite_as_sincOs,|jt|jtd|jtd|jSNrMrN)rrr4r r2rrPr#r#r$_eval_rewrite_as_cosIs  zTWave._eval_rewrite_as_coscOsDtd\}}}}td}t||||d||t||||dS)Nzmu, epsilon, x, tEr,)r rr)r)r'rQmuepsilonrMrNrUr#r#r$_eval_rewrite_as_pdeMs,zTWave._eval_rewrite_as_pdecOs0|jtt|jtd|jtd|jSrS)rrr r4r r2rrPr#r#r$_eval_rewrite_as_expRs   zTWave._eval_rewrite_as_exp)r8 __module__ __qualname____doc__r Zeror rpropertyrrrrrr0r1r2r4r9__repr__r?r@rDrFrJrKrLrRrTrXrYr#r#r#r$rsL?            N)$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_tor/rr#r#r#r$s