DOING PHYSICS WITH MATLAB

ANIMATION OF A TRAVELLING TRANSVERSE WAVE

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wm_ttw.m

An animation of a one-dimensional travelling wave is displayed. The animation can be saved as an animated gif file or as a avi file by setting the value the parameter flagA. The saved animated gif files and avi files can be used for display purposes and embedded in html documents. The advantage of the avi files is the animations can be repeatedly stopped and restarted.

wm_tt2.m

A [3D] view of a one-dimensional wave propagating in the Z direction which is described by the wavefunction .

The first-dimension corresponds to time t, the second-dimension to z and the third-dimension the value of the wavefunction .

[1D] TRAVELLING HARMONIC WAVE

A [1D] travelling harmonic wave can be represented by the wavefunction y(z,t) that is periodic both in space (z) and time (t). The profile of the travelling wave is sinusoidal at any instant and each point in the track of the wave performs simple harmonic motion. The wave function y(z,t) is given by equation 1.

(1)

(2)

where A is the amplitude, k is the propagation constant (or wave number), is the wavelength, is the angular frequency, f is the frequency, T the period and v is the phase or wave velocity. The - sign describes a wave propagating to the right and the + sign for a wave propagating to the left.

It is not possible to draw a simple graph of the wavefunction given by equation 1. So, animations of travelling waves can play a very important role to help improve one’s understanding of the mathematical description of travelling waves.

What do the animations tells us about the physics and mathematics of the motion of travelling waves?

· Easily distinguish between particle velocities in the medium and the wave velocity of the disturbance. The velocities are orthogonal to each other. The wave velocity is constant whereas the particle velocities vary both in direction and time.

· The variation is both space and time are displayed in the animations and the concepts of wavelength and period can be easily presented.

· The connection between the wave velocity and other parameters can be easy deduced from the animations.

· The phase of the wave in both space and time are displayed. Only the particles which are separated by integer multipes of a wavelength vibrate in phase.

ANIMATED GIFS

[3D] view of a one-dimensional wave propagating in the Z direction

A [3D] view of a one-dimensional wave propagating in the Z direction which is described by the wavefunction can be viewed graphically using the script

wm_ttw2.m. The first-dimension corresponds to time t, the second-dimension to z and the third-dimension, the value of the wavefunction . The meshgrid command is used to create the XY grid and the mesh command for displaying the [3D] plot. Sample graphical results are displayed in the following figures.

Changing the phase f shift the positions of the crests and troughs.

John A Sims

john.sims@ufabc.edu.br

Universidade Federal do ABC

http://www.ufabc.edu.br/

Biomedical Engineering Department,

Centro de Engenharia, Modelagem e Ciencias Sociais Aplicadas.

(Centre for Engineering, modelling and applied social sciences)

Rua Arcturus (Jd Antares)

Anchieta

09606070 - Sao Bernardo do Campo, SP - Brasil

Ian Cooper

matlabvisualphysics@gmail.com