Standing Waves in Pipes and on Strings

Physics II , March 2004

 

http://members.cox.net/gilvick/    Physics Home Page.

 

This investigation uses applets to demonstrate the composition of standing waves in pipes and on a string with attention to the harmonics generated by each.

 

Bring up physics home page and select the #1 applet.  This shows the standing waves in 3 kinds of pipes and the harmonics generated by each kind of pipe.  We will investigate.

OPEN PIPE

 

  1. Select “Both Sides Open” and “Displacement”.  The length of the pipe is 1 meter, the wavelength is 2 meters, the frequency is 172 Hz.  What is the velocity of sound in the pipe?
  2. Select “Higher” to get the first overtone.  Explain what you find.  Repeat for higher harmonics.
  3. Bring up applet #3 (Flute) and investigate the shape of the wave for each of the harmonics and the sum of the harmonics.
  4. Explain the symmetry of the waves with odd and even harmonics added in.

 

CLOSED PIPE

1.      Select “one side open” and “displacement”.  What is the fundamental frequency.  What is the relationship between the first overtone and the fundamental.  Look at next 3 overtones and explain the relationship.  What is the speed of sound in this pipe?

  1. Investigate the flute using only odd harmonics.  What do you see?  (Symmetry)?

 

BOTH SIDES CLOSED PIPE

What do you see here?  Useful?

STRING

Load applet #2 (Violin String) and investigate the behavior of the string as harmonics are added to the standing wave.  Explain symmetry. 

 

INTERFEARENCE

Select Applet #4 and investigate the submenu items “Wave interference 1” etc.

 

These patterns illustrate that the resultant wave is the algebraic sum of the individual waves.  Explain?