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.

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)