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)

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)