# 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 is represented as $$A \times cos(k*x - \omega \times t + \phi )$$, where $$A$$ is the amplitude, $$\omega$$ is the angular velocity, $$k$$ 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.

Raises

ValueError : When neither frequency nor time period is provided

or they are not consistent.

TypeError : When anything other than TWave objects is added.

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*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*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 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)