This lecture covers selected parts of sections 1-1 through 1-4 of McQuarrie:
The classical wave equation describes wave motion of many classical systems including a vibrating string fixed at both ends. This equation is a linear partial differential equation whose solution is the amplitude of a wave as a function of spatial coordinates and time.
The solution of the wave equation subject to specific initial and boundary conditions is solved by the finite difference method. A MATLAB script is developed that allows arbitrary initial and boundary conditions to be input by the user.
To illustrate the use of the MATLAB script, we solved the wave equation for plucking a string under tension, fixed at both ends. The first case treated the problem of a triangular dispacement as in McQuarrie Figure 4-3. The second case used a sinusoidal displacement to excite only one of the allowed frequencies of the system.(See McQuarrie, Figure 2-3). The third case used a square dispacement. Here, two square pulses, each traveling in the opposite direction were produced.
Click here to see a copy of the M-file for this Lecture. This m file and all of the others have line breaks missing. Do not "save" the file. Instead, highlight the entire text and copy and paste it into the MATLAB editor (select a new M file in the File menu of MATLAB first). Now the script will have line breaks and you can do a " save as" to save it as a named file.
Click here to down load a copy of the binary Word file for this Lecture. PC users can double click on the file to open it in word. Mac folks will have to open word and then open the file.