Ejs Open Source Standing Wave in Pipes Model Java Applet /htdocs/ntnujava/ejsuser/14019/users/sgeducation/pipewee01_pkg/pipewee01.propertiesFull screen applet or Problem viewing java?Add http://www.phy.ntnu.edu.tw/ to exception site list
http://www.compadre.org/osp/items/detail.cfm?ID=7878 Ejs Standing Waves in a Pipe Model
written by Juan Aguirregabiria
[s]http://www.opensourcephysics.org/items/detail.cfm?ID=7880 Ejs Resonance in a Driven String Model
written by Juan Aguirregabiria [/s]
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Standing waves in a pipe by Juan Aguirregabiria
Let us consider a narrow pipe along the OX axis. Each end may be open or closed. The simulation will display the first 5 normal modes, which are
u(t,x) = A sin(n ? x) cos(? t + ?) when both ends are closed.
u(t,x) = A sin((n-1/2) ? x) cos(? t + ?) when the left end is closed and the right end open.
u(t,x) = A cos((n-1/2) ? x) cos(? t + ?) when the left end is open and the right end closed.
u(t,x) = A cos(n ? x) cos(? t + ?) when both ends are open.
Units are arbitrary.
Below you may choose the mode n = 1, ...,5, as well as the animation step ?t.
The upper animation shows the displacement field u(t,x) and the pressure p(t,x) as functions of x at each time t.
In the lower animation you may see the evolution of the position x + u(t,x) of several points and a contour plot of p(t,x) (lighter/darker blue means higher/lower pressure).
Optionally one can see the nodes where the displacement wave vanishes at all times.
Scale has been arbitrarily enhanced to make things visible; but keep in mind that we are considering very small displacements and pressure changes in a narrow pipe.
Put the mouse point over an element to get the corresponding tooltip.
Activities by Juan Aguirregabiria
Compute the position of the nodes for mode number n in the four considered cases.
Use the simulation to check your calculation.
Where are the pressure nodes in the different cases?
Which is the relationship between the displacement and pressure waves? How does it appears in the animation?
This is an English translation of the Basque original for a course on mechanics, oscillations and waves. It requires Java 1.5 or newer and was created by Juan M. Aguirregabiria with Easy Java Simulations (Ejs) by Francisco Esquembre. I thank Wolfgang Christian and Francisco Esquembre for their help.
lookang also thank Juan M. Aguirregabiria for sharing such a useful computer model!
customization is below.
1. Musical instruments make use of stationary waves to create sound.
2. All strings (or pipes) have a natural frequency also known as the resonant frequency, which is related to the length of the string (or pipe).
3. The resonant frequencies can be determined using the following rules:
a. The two ends of a guitar string do not move and hence they must always be nodes.
b. The air molecule at any closed end of the pipe does not move and hence it must always be a node.
c. However, if the end of the pipe is open, the air molecule has the room to vibrate about the equilibrium position at maximum amplitude. This location is an antinode.