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Easy Java Simulations (2001- ) => Collaborative Community of EJS => Topic started by: lookang on November 04, 2011, 02:21:42 pm



Title: Ejs Open Source Standing Wave in Pipes Model Java Applet
Post by: lookang on November 04, 2011, 02:21:42 pm
Ejs Open Source Standing Wave in Pipes Model Java Applet

reference:
http://www.compadre.org/osp/items/detail.cfm?ID=7878 Ejs Standing Waves in a Pipe Model
written by Juan Aguirregabiria
http://www.opensourcephysics.org/items/detail.cfm?ID=7880 Ejs Resonance in a Driven String Model
written by Juan Aguirregabiria
[ejsapplet]
collecting helpful ideas for remix later


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 π x) cos(ω t + δ) when both ends are closed.
u(t,x) = A sin((n-1/2) π x) cos(ω t + δ) when the left end is closed and the right end open.
u(t,x) = A cos((n-1/2) π x) cos(ω t + δ) when the left end is open and the right end closed.
u(t,x) = A cos(n π x) cos(ω t + δ) when both ends are open.
Units are arbitrary.
Below you may choose the mode n = 1, ...,5, as well as the animation step Δt.
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.


Title: Re: Ejs Open Source Resonance and Stationary Wave in Strings Model Java Applet
Post by: lookang on November 04, 2011, 02:26:12 pm
Recall:
Distance between node and adjacent antinode,  NA = wavelength/4
Distance between 2 adjacent nodes, NN = Distance between 2 adjacent anti-nodes, AA =  wavelength/2

Inquiry 5: We draw waves in a pipe as sinusoidal in shape like that in above graphs.
What should the two “axes” of the graphs be?


In musical instruments, the simplest mode of vibration is the fundamental frequency, f1. This is the lowest possible frequency.  This determines the frequency of the note produced since the waveform has the largest amplitude compared with the other modes of vibrations. Frequency f2 is the next higher possible frequency followed by f3. It is the superposition of all the possible modes of vibration that causes different instruments to sound different.

Eg 4 An organ pipe of effective length 0.60 m is closed at one end. Given that the speed of sound in air is 300 m s-1. Find the two lowest resonant frequencies.


Solutions:
For fundamental mode of vibration, Length of pipe, l = NA =  
      0.60 =     wavelength/4 = 2.4 m
v = f * wavelength
300 = f (2.4)
f = 125 Hz

For 1st overtone (next “complex” mode of vibration), Length of pipe, l = NANA =  
      0.60 =     3*wavelength/4 = 0.80 m
v = f *wavelength
300 = f (0.80)
f = 375 Hz


Eg 5 The Tacoma Bridge was an 850 m long suspension bridge built across a river. The speed of transverse waves along the span of the bridge was 400 m s1. Find the most possible frequency of the wind that caused the collapse of the Tacoma Bridge if it was vibrating at its fundamental frequency

Solutions:

wavelength/2  = L
wavelength = 2*850 = 1700 m

since v = f* wavelength
400 = f*1700
0.24 Hz = f

 
The bridge collapsed as resonance set in.
therefore Driving frequency of wind = fundamental frequency of bridge vibration = 0.24 Hz



Title: Re: Ejs Open Standing Wave in Pipes Model Java Applet
Post by: lookang on January 09, 2012, 10:49:46 pm
changes:

9 jan 2012
design layout to usual bottom
A = 0.49 instead of 0.4 previously to make same as lecture notes
add Nodes texts and extra
add Antinodes text and extra
add v = f*lambda assuming speed of sound is 330 m/s
10 Jan 2012
add modeling component through drop-down menu and input field for learners to key in equations to understand the standing waves formed
readjusted position of pipes and everything to start at y = 0 instead of the previous y =0.5 for ease of modeling
add length of pipe for calculation purpose, visualization does not change

enjoy!


Title: Re: Ejs Open Source Standing Wave in Pipes Model Java Applet
Post by: lookang on October 04, 2013, 10:24:32 pm
changes
http://weelookang.blogspot.sg/2013/10/longitudinal-sound-wave-in-pipe-model.html

changes made:

9 jan 2012 Design layout to usual bottom
A = 0.49 instead of 0.4 previously to make same as lecture notes
add Nodes texts and extra
add Antinodes text and extra
add v = f*lambda assuming speed of sound is 330 m/s
10 Jan 2012 add modeling component through drop-down menu and input field for learners to key in equations to understand the standing waves formed
readjusted position of pipes and everything to start at y = 0 instead of the previous y =0.5 for ease of modeling
3 October 2013 reduce the number of air molecules representation (RED) to draw to 19 and thicken the lines
added text into actual frames "u(t,x) displacement" and "p(t,x) pressure"
add text pipe side view
add text "pressure variation BLACK=-1, BRIGHT=+1 "
add dt= slider to allow slowing slow of the simulation
added boundary or envelope of the amplitude in dark-grey
made u(x,t) and p(x,t) appears as the check-box is selected


http://weelookang.blogspot.sg/2013/10/longitudinal-sound-wave-in-pipe-model.html
https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejs_pipewee02.jar
author: Juan Aguirregabiria and lookang (this remix version)
Key features designed:
Symbolic text to support visuals NAN, node, anti node node etc.
Can simulate closed or open end of a pipe
Microscopic visual of molecules enhanced with order and random position referencing tat leong codehttps://dl.dropbox.com/s/y8xsj6zx4xaqsur/ejs_longitudinal_waves_leetl_wee_v3.jar
dt for slowing and speed up simulation
amplitudes for envelope of displacement visuals
pressures for learning of real equipment sound detector to be placed at the maximum/minimum pressure from the ambient atmospheric as highlighted by kian wee
inputs field for calculation of any length of pipe
modelling-mathematical features as highlighted by peng poo and oon how as key to deepening learning


Title: Re: Ejs Open Source Standing Wave in Pipes Model Java Applet
Post by: lookang on October 04, 2013, 10:35:34 pm
dear professor hwang,

i cannot upload the new jar file already on the top first post
could u kindly check the forum for bug?
thanks!