We watched all the videos and are confused because the summary basically says exactly the opposite of the teaching videos where the drawings of nodes and antinodes are concerned. THe videos say that in an open tube the node would be directly in the middle with the antinodes at either end "dancing around wildly." But the diagram in the summary shows the opposite. The teaching video states that a closed tube has one node at the closed end of the tube with the antinode being on the open end. The summary says the node in a closed tube would be at the open or closed end with the antinode being in the middle- I'm confused.

Hi Karen! I think you are confused between the two different diagrams given for each open and closed tubes. The first diagram for each is of the displacement of air molecules which is we use to calculate the wavelength. On the other hand, the second diagram for each represents the air pressure variation around the tubes (which we needn't be concerned for any calculation purpose!). Consider the fig 2 i.e for air pressure variation in open tubes. At the ends air pressure is equal to the atmospheric pressure. Since air molecules can’t oscillate at displacement nodes (in the middle) to equalize pressure, displacement nodes have maximum pressure variations. So is the graph shown. Please read the whole text carefully. Cheers!

Main content

Course: AP®︎/College Physics 1 > Unit 9

Lesson 5: Introduction to sound

Introduction to sound review

Google Classroom

Review the key terms and skills for sound waves, including how to identify the nodes and antinodes for standing waves in tubes.

Key terms

Term	Meaning
Open tube	Tube that is open at both ends. Also called an open pipe.
Closed tube	Tube that is open at one end, and closed at the other. Also called a closed pipe.
Resonance	Another term for standing sound waves.

Standing sound waves open and closed tubes

Sound waves are longitudinal waves in a medium such as air. The molecules in the medium vibrate back and forth from their equilibrium position. This leads to the molecules being compressed in some parts of the wave, which results in variations in pressure in a predictable pattern. For example, when a musician blows into a tube such as a flute, the sound produced comes from waves that travel along the length of the tube.

Just like other waves, the energy of sound waves increases with the wave amplitude. The loudness or volume of the sound also increases with wave amplitude.

In open and closed tubes, sounds waves can exist as standing waves as long as there is at least one node.

Open tubes

In an open tube, the medium (ex. air) at the open ends vibrates horizontally parallel to the tube length. This means the standing wave has displacement antinodes at the ends of the tube for all harmonics, and a node in the middle for the fundamental.

The simplest standing wave in an open tube is the fundamental, which has

2

antinodes and

1

node. Thus, there is half of a wavelength between the antinodes. For an open tube with length

L

, the wavelength

λ

of the standing wave that corresponds with the fundamental frequency is:

\begin{aligned} L & = \frac{λ}{2} \\ λ & = 2 L \end{aligned}

Where the fundamental frequency is:

\begin{aligned} f_{1} & = \frac{v}{λ} \\ f_{1} & = \frac{v}{2 L} \end{aligned}

Standing waves with any integer multiple of the fundamental frequency can fit in an open tube.

Another way to think about standing waves in open tubes is by instead considering how the air pressure varies along the length of the tube. For open tubes, the air pressure at the ends equalizes with the atmosphere. Thus, the pressure stays constant at the open ends and they are pressure nodes.

The open end of a tube is a pressure node as well as a displacement antinode. This is admittedly confusing. The pressure at the open end of a tube has a fixed constant value (i.e node) equal to one atmosphere (assuming your tube is exposed to the air near Earth's surface). But the displacement of the air molecules at the open end of the tube has a maximally varying value (i.e. antinode) since the air is free to move at the open end. In other words, if you're drawing a diagram of the pressure in the tube, the open ends will be nodes. If you're drawing a diagram of the displacement of the air in the tube, the open ends will be antinodes.

Closed tubes

The air molecules are not free to vibrate back and forth parallel to the tube, so the displacement standing wave has is a node at the closed end. The open end of the tube is always an antinode since the air molecules can vibrate horizontally parallel to the length of the tube.

The simplest standing wave case in a closed tube has

1

antinode and

1

node. Thus, there is one quarter of a wavelength between the antinodes.For a closed tube with length

L

, the standing wave that corresponds with the fundamental frequency is:

\begin{aligned} L & = λ / 4 \\ λ & = 4 L \end{aligned}

The fundamental frequency is:

\begin{aligned} f_{1} & = \frac{v}{λ} \\ f_{1} & = \frac{v}{4 L} \end{aligned}

For closed tubes, we can have only odd-numbered harmonics. That’s because closed tubes by definition have a node at one end and antinode at the other, so there’s no way for even-numbered frequencies to be present.

We can also think about standing waves in closed tubes in terms of the air pressure along the length of the tube. For closed tubes, the air pressure at the closed end varies since it does not need to equalize with the atmosphere. The pressure at the open end is constant, so the pressure wave has a node at the open end and an antinode at the closed end.

Common mistakes and misconceptions

Sometimes people forget that sound waves require a medium. Sound waves can’t travel through a vacuum (empty space) because there are no air molecules to vibrate and cause pressure variations.

Learn more

For deeper explanations of sound waves, see our videos:

To check your understanding and work toward mastering these concepts, check out our exercises:

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CrankyPhotons
Posted 4 years ago. Direct link to CrankyPhotons's post “Can you please upload a v...”
Can you please upload a video on pressure and displacement nodes and antinodes?
It's a bit confusing to master this concept.
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(24 votes)
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fatama.rahman1
Posted 4 years ago. Direct link to fatama.rahman1's post “did anyone else think tha...”
did anyone else think that the questions were hard and that it had nothing to do with the videos?
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(20 votes)
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Karen Knowlton
Posted 5 years ago. Direct link to Karen Knowlton's post “We watched all the videos...”
We watched all the videos and are confused because the summary basically says exactly the opposite of the teaching videos where the drawings of nodes and antinodes are concerned. THe videos say that in an open tube the node would be directly in the middle with the antinodes at either end "dancing around wildly." But the diagram in the summary shows the opposite. The teaching video states that a closed tube has one node at the closed end of the tube with the antinode being on the open end. The summary says the node in a closed tube would be at the open or closed end with the antinode being in the middle- I'm confused.
Button navigates to signup pageComment on Karen Knowlton's post “We watched all the videos...”
(12 votes)
Answer
- Anurag Debnath
  Posted 5 years ago. Direct link to Anurag Debnath's post “Hi Karen! I think you are...”
  Hi Karen!
  I think you are confused between the two different diagrams given for each open and closed tubes. The first diagram for each is of the displacement of air molecules which is we use to calculate the wavelength. On the other hand, the second diagram for each represents the air pressure variation around the tubes (which we needn't be concerned for any calculation purpose!).
  Consider the fig 2 i.e for air pressure variation in open tubes. At the ends air pressure is equal to the atmospheric pressure. Since air molecules can’t oscillate at displacement nodes (in the middle) to equalize pressure, displacement nodes have maximum pressure variations. So is the graph shown. Please read the whole text carefully. Cheers!
  Button navigates to signup page
  (10 votes)
Nightmare252
Posted 5 years ago. Direct link to Nightmare252's post “So nodes are where waves ...”
So nodes are where waves change direction and anti nodes are crests of waves right?
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(4 votes)
Answer
kolyier reed
Posted a year ago. Direct link to kolyier reed's post “Not a question, just a wa...”
Not a question, just a warning/tip!!
Some of the visuals on the "practice: pressure and displacement of sound waves in tubes" are off/wrong. There displacement anti-nodes at closed ends of tubes, when there can only be nodes and vice-versa for open ends. Go with your intuition, not what the visuals/pictures show!
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(2 votes)
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hannahbuckley123
Posted 3 years ago. Direct link to hannahbuckley123's post “I am super confused about...”
I am super confused about pressure and displacement nodes and antinodes. I had the idea that if it were a pressure antinode, it would be a displacement node, but the practices make it seem that if it is a pres. node, its also a displ. node. Which ones are nodes and antinodes for pressure and displacement?
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(2 votes)
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cjgorski
Posted 6 months ago. Direct link to cjgorski's post “Why do we have to do coll...”
Why do we have to do college stuff in 6th grade?
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(1 vote)
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- M.albolushi24
  Posted 3 months ago. Direct link to M.albolushi24's post “because we are asian that...”
  because we are asian that's why my friend
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  (1 vote)
Kevin Liang
Posted 3 years ago. Direct link to Kevin Liang's post “So a displacement node is...”
So a displacement node is when there is no displacement, which is caused by the counteracting pressure from both sides, which is also the place with the greatest oscillation of pressure, so-called pressure antinode?

And a displacement antinode is when there is a maximum oscillation of displacement. So at this point, the air is moving relatively along with the surrounding air, which leads to approximately constant pressure, so-called pressure node?
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(1 vote)
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Gift Owolabi
Posted 4 years ago. Direct link to Gift Owolabi's post “Not a question, just a wa...”
Not a question, just a warning/tip!!
Some of the visuals on the "practice: pressure and displacement of sound waves in tubes" are off/wrong. There displacement anti-nodes at closed ends of tubes, when there can only be nodes and vice-versa for open ends. Go with your intuition, not what the visuals/pictures show!
Button navigates to signup pageButton navigates to signup page
(0 votes)
Answer
0543820
Posted a year ago. Direct link to 0543820's post “displacement node”
displacement node
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