Thursday, October 3, 2013

Longitudinal Sound Wave in Pipe Model by Juan M. Aguirregabiria




Longitudinal Sound Wave in Pipe Model by Juan M. Aguirregabiria and now lookang (this legally remixed version).
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, lookang also thank Fu-Kwun Hwang, Wolfgang Christian and Francisco Esquembre for their invaluable help for which i have learnt so much from their work.!


closed-closed pipe system in 5th harmonic

author: Juan Aguirregabiria and lookang (this remix version)
Key features designed:
  1. Symbolic text to support visuals NAN, node, anti node node etc.
  2. Can simulate closed or open end of a pipe
  3. 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
  4. dt for slowing and speed up simulation 
  5. amplitudes for envelope of displacement visuals
  6. 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
  7. inputs field for calculation of any length of pipe
  8. modelling-mathematical features as highlighted by peng poo and oon how as key to deepening learning



author: Juan Aguirregabiria and lookang (this remix version)
Key features designed:
  1. Symbolic text to support visuals NAN, node, anti node node etc.
  2. Can simulate closed or open end of a pipe
  3. 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
  4. dt for slowing and speed up simulation 
  5. amplitudes for envelope of displacement visuals
  6. 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
  7. inputs field for calculation of any length of pipe
  8. modelling-mathematical features as highlighted by peng poo and oon how as key to deepening learning


author: Juan Aguirregabiria and lookang (this remix version)
Key features designed:
  1. Symbolic text to support visuals NAN, node, anti node node etc.
  2. Can simulate closed or open end of a pipe
  3. Microscopic visual of molecules
  4. dt for slowing and speed up simulation 
  5. amplitudes for envelope of displacement visuals
  6. 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
  7. inputs field for calculation of any length of pipe
  8. modelling-mathematical features as highlighted by peng poo and oon how as key to deepening learning


http://weelookang.blogspot.sg/2012/01/ejs-open-standing-wave-in-pipes-model.html
https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejs_pipewee01.jar
author: Juan Aguirregabiria and lookang (this remix version)





changes made:

  1. 9 jan 2012 Design layout to usual bottom
  2. A = 0.49 instead of 0.4 previously to make same as lecture notes
  3. add Nodes texts and extra
  4. add Antinodes text and extra
  5. add v = f*lambda assuming speed of sound is 330 m/s
  6. 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
  7. readjusted position of pipes and everything to start at y = 0 instead of the previous y =0.5 for ease of modeling
  8. 3 October 2013 reduce the number of air molecules representation (RED) to draw to 19 and thicken the lines
  9. added text into actual frames "u(t,x) displacement" and "p(t,x) pressure"
  10. add text pipe side view
  11. add text "pressure variation BLACK=-1, BRIGHT=+1 "
  12. add dt= slider to allow slowing slow of the simulation
  13. added boundary or envelope of the amplitude in dark-grey
  14. made u(x,t) and p(x,t) appears as the check-box is selected
closed-closed pipe system in 1st harmonic

closed-closed pipe system in 2nd harmoni

closed-closed pipe system in 3rd harmonic

closed-closed pipe system in 4th harmonic

closed-closed pipe system in 5th harmonic



closed-closed pipe system in 1st harmonic random molecules representation

closed-closed pipe system in 2nd harmonic random molecules representation

closed-closed pipe system in 3rd harmonic random molecules representation

closed-closed pipe system in 4th harmonic random molecules representation

closed-closed pipe system in 5th harmonic random molecules representation


closed-closed pipe system in 1st harmonic

closed-closed pipe system in 2nd harmonic

closed-closed pipe system in 3rd harmonic

closed-closed pipe system in 4th harmonic

closed-closed pipe system in 5th harmonic





closed-closed pipe system in 1st harmonic

closed-closed pipe system in 2nd harmonic

closed-closed pipe system in3rd harmonic

closed-closed pipe system in 4th harmonic

closed-closed pipe system in 5th harmonic


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.

contribution to wikipedia:


Harmonics and overtones


The tight relation between overtones and harmonics in music often leads to their being used synonymously in a strictly musical context, but they are counted differently leading to some possible confusion. This chart demonstrates how they are counted:
Harmonics are not overtones, when it comes to counting. Even numbered harmonics are odd numbered overtones and vice versa

FrequencyOrderName 1Name 2Wave RepresentationMolecules Representation
1 · f =   440 Hzn = 1fundamental tone1st harmonic

Pipe001

Molecule1
2 · f =   880 Hzn = 21st overtone2nd harmonic

Pipe002

Molecule2
3 · f = 1320 Hzn = 32nd overtone3rd harmonic

Pipe003

Molecule3
4 · f = 1760 Hzn = 43rd overtone4th harmonic

Pipe004

Molecule4
.