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# Standing waves in closed tubes

Explore the intriguing world of sound waves in open and closed tubes! This lesson breaks down how the length of a tube influences the wavelength and frequency of sound, revealing why you hear different notes as you sip your soda. Discover the unique patterns of harmonics in open-closed tubes, and how they differ from open-open tubes. Created by David SantoPietro.

## Want to join the conversation?

• Musicians sometimes talk about going up or down an octave. How do the concepts of the resonance region, anti-nodes, and nodes relate to the idea of an octave?
• every power of 2 * 1st harmonic is an octave above. For example:
880 = A in 2nd octave
440 = A in first octave
220 = A in small octave
110 = A in great octave
• If I have a cylindrical container open-open and another one open-close (that are identical), which one will produce lower notes? And why?
• If we consider that both of them are first harmonic, then "open open" will be higher.
As wavelength for "open open" (2L) is less than for "open close" (4L)..
• Not quite understanding why there can only be an odd number of nodes.
• it depends on the situation.

you can draw a standing wave (indeed create a standing wave using a spring) with odd and even number of nodes.

what makes you think there can only be odd numbers of nodes??

take a look online for examples

if you look here at 5.52, the standing wave has 10 nodes

• How does this apply to windpipe instruments? Like... I used to play the clarinet (and recorder in elementary school) but generally, the more holes you plug the lower the note. So if you don't plug any holes in the windpipe instrument then the L is shorter? Super random question, I know lol.
• Yes, by covering or opening various holes you are changing the place where the nodes are in the standing wave.
• Can we just count the number of antinodes and nodes and leave out the one at the open end and get n?
Like for the 3rd harmonic, we have 2 nodes and 1 antinode before the last antinode, so that makes a total of three, thus 4L / 3.
For the fifth harmonic, there are 3 nodes and 2 antinodes other than the last antinode, so that is a total of 5. Thus 4L / 5.
I mean I think this helps during exams. Just skip the antinode at the opening an count the other nodes and antinodes to get n. It works right?
but to have a bit more concise equation
we better focus on nodes only

0. n = number of nodes in the middle (except for the two edges)
1. open-open tube
wavelength = 4L/2n
2. open-closed tube
wavelength = 4L/(2n+1)
3. closed-closed tube (e.g. a string with two standing edges)
wavelength = 4L/2n

one more thing, the difference between case1 and case3 is the type of starting (and ending) nodes. 1 starts and ends at the antinodes, while 3 at nodes
(1 vote)
• I'm not quite sure on how to name the harmonics in this system. Do you call the harmonic where n=3 the 2nd or 3rd harmonic? Is n=5 the 3rd or 5th?
• If I blow air over a soda bottle, how do i know which harmonic I am playing? Is there a way to know how many nodes are in in there?
And what can I do to get the overtone of the current tone(like blow harder or softer..)?
• what is meant by fundamental harmonic, second harmonic and so on. What is the relation between them? Do they occur at the same time or turn by turn? what effect is caused by them?
(1 vote)
• The fundamental is the same thing as the first harmonic, and it is the mode of vibration where you have the fewest possible nodes in the standing wave. The second harmonic is the next highest frequency where you can get a standing wave. The third harmonic is the next, etc.