Organ pipes

The following animation examines the sound waves with in, and near the axis, of an organ pipe. The axis of the pipe can be thought of as the horizontal line which passes through the center of the animation. The sound waves produced by the pipe are variations in air pressure that propagate in the direction of the pipe's axis. White regions indicate areas in which the pressure is a maximum while black regions indicate areas in which the pressure is a minimum.

The animation allows you to study the sound waves produced by the organ pipe from three different perspective (i.e., modes). Select the mode you are interested by using the form box in the lower right hand corner of the animation. The modes from which you may choose from are as follows:

• U-Drag-It Mode: In this mode the pressure variations are produced by a movable piston. This piston is shown in red on the left end of the animation. Place your mouse over the piston and drag it right and left alternatively. Notice that the regions immediately to the right of the piston become lighter as you drag the piston to the right. This is because the air with in the pipe will be compressed as you drag it to the right. Conversely, notice that the regions immediately to the right of the piston become darker as you drag the piston to the left. This is because the air with in the pipe will be rarified as you drag it to the left.
• Analytic Mode: This mode focuses more on the description of the sound waves as opposed to how these waves were produced. This mode displays the sound wave associated with the pressure variations indicated by the text box marked P(x,t) (P denoting pressure, x denoting the x coordinate, t denoting time) appearing at the bottom of the animation. By default, the animation displays a pressure variation given by P(x,t)=sin(0.5*x-3*t). This pressure variation represents a sound wave traveling to the right at a speed of 3/0.5=6. The wavelength of the wave is equal to 2*(3.14)/0.5=12.56 and the frequency of the wave is equal to 2*(3.14)*3=18.84. You may wish to look at the following situations (don't forget to type in asterisk, *, between the constants and the variables x and t).
  • How does the wave change if you replace 0.5 by 2? That is, set the pressure variation equal to sin(2*x-3*t).
  • How does the wave change if you replace 3 by 6? That is, set the pressure variation equal to sin(2*x-6*t).
  • How does the wave change if you multiply sin(0.5*x-3*t) by 10? That is, set the pressure variation equal to 10*sin(2*x-3*t).
  • How does the wave change if you replace minus sign by a plus sign? That is, set the pressure variation equal to sin(2*x+3*t).
  • Consider the pressure variation given by sin(0.5*x)*sin(3*t). How does this situation differ from the original, default situation?
• Source Mode: In this mode you enter the pressure variation that occurs near the source with in the organ pipe that produces the sound waves. As a result of this, you must only enter a pressure variation which is a function of t, but NOT of x.