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# Introduction to sound review

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

## Key terms

TermMeaning
Open tubeTube that is open at both ends. Also called an open pipe.
Closed tubeTube that is open at one end, and closed at the other. Also called a closed pipe.
ResonanceAnother 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 lambda of the standing wave that corresponds with the fundamental frequency is:
\begin{aligned}L&= \dfrac{\lambda}{2}\\ \\\\ \lambda &= 2L\end{aligned}
Where the fundamental frequency is:
\begin{aligned}f_1 &= \dfrac{v}{\lambda}\\ \\\\ f_1 &= \dfrac{v}{2L}\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.

### 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 &= {\lambda}/{4}\\ \\\\ \lambda &= 4L\end{aligned}
The fundamental frequency is:
\begin{aligned}f_1 &= \dfrac{v}{\lambda}\\ \\\\ f_1 &= \dfrac{v}{4L}\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.

For deeper explanations of sound waves, see our videos:
To check your understanding and work toward mastering these concepts, check out our exercises:

## Want to join the conversation?

• Can you please upload a video on pressure and displacement nodes and antinodes?
It's a bit confusing to master this concept. • did anyone else think that the questions were hard and that it had nothing to do with 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. • 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!
• So nodes are where waves change direction and anti nodes are crests of waves right? • 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? • 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?    