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.

Raises:

ValueError : When neither frequency nor time period is provided

or they are not consistent.

TypeError : When anything other than TWave objects is added.

Explanation

It is represented as \(A \times cos(k*x - \omega \times t + \phi )\), where \(A\) is the amplitude, \(\omega\) is the angular frequency, \(k\) is the wavenumber (spatial frequency), \(x\) is a spatial variable to represent the position on the dimension on which the wave propagates, and \(\phi\) is the phase angle of the wave.

Arguments

amplitudeSympifyable: Amplitude of the wave.
frequencySympifyable: Frequency of the wave.
phaseSympifyable: Phase angle of the wave.
time_periodSympifyable: Time period of the wave.
nSympifyable: Refractive index of the medium.

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

property 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

property angular_velocity¶

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

property frequency¶

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

property n¶: Returns the refractive index of the medium

property phase¶

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

property speed¶

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)

property time_period¶

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

property wavelength¶

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)

property wavenumber¶

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)