# Acoustics and Vibration Animations

Daniel A. Russell, Graduate Program in Acoustics, The Pennsylvania State University

Based on a work at http://www.acs.psu.edu/drussell/demos.html.

The content of this page are a work in progress. The first draft of this content was originally posted on September 21, 2023.

The animations and content on this page were developed at the request of Susannah Levi (Communicative Sciences and Disorders Dept., New York University, https://wp.nyu.edu/Levi/)
This work was supported by a Teaching Advancement Grant from New York University's Center for Faculty Advancement, awarded to Susannah Levi in 2023.

# What happens at open and closed ends of a pipe?

## Closed End

Displacement is zero at a closed end. The displacement wave pulse reverses direction and the amplitude is inverted, but pressure reflects without inversion (no phase change). When the wave hits the fixed end the final spring is compressed twice as much so it pushes back hard and the wave reverses direction.

As the wave pulse travels to the right toward the closed end, the leading edge of the wave is the compressed (squished) spring, followed by a stretched spring. After it reflects from the closed (fixed) end, the wave simply reverses direction, so that the leading edge (now traveling to the left) is still a compressed spring, with a stretched spring following behind. The red arrow indicates the leading edge of the wave pulse. The light blue plot above the springs shows the longitudinal displacement, and the light red plot below the springs shows the pressure (higher when springs are compressed and lower when springs are stretched).

## Open End

Displacement is maximum at an open end. The displacement wave pulse reverses direction but remains upright (no phase change) while pressure is inverted upon reflection (180o phase change). When the final mass passes beyond the opening at the end of the pipe, the spring it is connected to pulls it back inside and the wave pulse travels back up the pipe.

As was the case for the animation above, the leading edge of the original wave travelign to the right is the compressed (squished) spring, followed by a stretched spring. But now, the reflected wave is inverted as it returns from the open end, so that the leading edge of the reflected wave (traveling to the left) is a stretched spring with a compressed spring following behind. The two sets of animations should be synced up so that they both start at the same time, and the phase difference between the two reflected waves should be apparent if you watch both animations together. The light blue plot above the springs shows the longitudinal displacement, and the light red plot below the springs shows the pressure (higher when springs are compressed and lower when springs are stretched).

## Comparing the Two Cases

Here are the two animations together so you can compare the relative phases after reflection from the two different pipe terminations