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Assuming the pipes are cylindrical.

\({D_2}\ /\ {D_1}\) = 1.5

Special Cases

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The change in impedance can range from +∞ to -∞ with interesting cases at either end and between.

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Exaggerate: 🛈

Make the displacement 3x larger. Note that the visual density will no longer align with the pressure plot.

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Adjust the point sizes proportional to pressure to visualize density.
Parcel Volume 🛈

The initial cross-sectional area is set to 1 so the particle and volume displacement have the same value even if the units are different.

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Parcel Volume 🛈

The initial cross-sectional area is set to 1 so the parcel and volume velocity have the same value even if the units are different.

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Each of these plots are normalized to the the incident wave. The units shown are simply to clarify the quantity plotted.
Intro

Whenever a wave encounters a change in impedance it will transmit through it, reflect from it, or a combination of the two. These plots show what will happen when the change in impedance is caused by the pipe a wave is traveling in changes size.

Interpreting the Plots

Before getting to the reflection, let's first discuss the plots. This is best done with the diameter ratio set to 1 or by selecting the "Constant Impedance" Special Case.

Example of Sparrowgram and displacement plot in a pipe with constant impedance
Figure 1 - Above is a sparrowgram of a continuous pipe. Below is a Guassian pulse of displacement which is applied to the points of the sparrowgram.

Note that the marks line up for 1 unit displacement

You need to understand that a positive area on the displacement plot corresponds to a parcel having moved to the right.

A Note About Accurate Sparrowgrams

in-progress

What is impedance

in-progress

parcel vs. Volume Displacement and Velocity

in-progress

This page is (for now) best viewed on a computer screen