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-
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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)-
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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).
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Consider the pressure variation
given by sin(0.5*x)*sin(3*t). How does this situation differ from the
original, default situation?
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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.
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