# 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, $$kis wavenumber, :math:x$$ 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[source]

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[source]

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[source]

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[source]

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[source]

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[source]

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[source]

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[source]

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)

Utilities

Unit systems