Waves¶
This module has all the classes and functions related to waves in optics.
Contains
- TWave
-
class
sympy.physics.optics.waves.
TWave
(amplitude, frequency=None, phase=0, time_period=None, n=n)[source]¶ 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 has been represented as A \times cos(k*x - \omega \times t + \phi ) where A is amplitude, \omega is angular velocity, k`is wavenumber, :math:`x is a spatial variable to represent the position on the dimension on which the wave propagates and \phi is phase angle of the wave.
Raises: ValueError : When neither frequency nor time period is provided
or they are not consistent.
TypeError : When anyting 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*m/(n*s) >>> w3.angular_velocity 2*pi*f
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.
-
amplitude
¶ 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
-
angular_velocity
¶ Returns angular velocity 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.angular_velocity 2*pi*f
-
frequency
¶ Returns the frequency 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.frequency f
-
phase
¶ Returns the phase angle 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.phase phi
-
speed
¶ Returns the speed of travelling wave. It is medium dependent.
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*m/(n*s)
-
time_period
¶ Returns the time period 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.time_period 1/f
-
wavelength
¶ Returns wavelength of the wave. 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*m/(f*n*s)
-
wavenumber
¶ Returns wavenumber 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.wavenumber pi*f*n*s/(149896229*m)