Sound Waves: Characteristics and Applications · Lesson 5 of 14
Graphical Representation of a Sound Wave
“A density graph turns invisible compressions and rarefactions into a readable wave pattern with crests and troughs.”
• Relate compressions and rarefactions to density variation. • Interpret a density-versus-distance graph. • Identify average density crest and trough. • Explain an alternative density-versus-time graph. • Convert a particle-density picture into a wave graph.
Compressions and rarefactions are regions of changing density, but drawing thousands of particles every time is inconvenient. A graph provides a compact way to represent these periodic density variations.
Graphical Representation of a Sound Wave
At one instant, plot distance from the source along the horizontal axis and density of the medium along the vertical axis. The average density is shown as a reference line. Where density rises above average, the wave is in a compression region. Where density falls below average, the wave is in a rarefaction region.
The highest point on the graphical representation, corresponding to maximum density in the representation used here.
The lowest point on the graphical representation, corresponding to minimum density.
The curve does not mean that air particles physically move up and down in space. The vertical direction is density on the graph. The actual particles in a longitudinal sound wave vibrate back and forth along the propagation direction.
Density Variation With Time
Another valid graph keeps the position fixed and shows how density changes with time as successive compressions and rarefactions pass that point. The horizontal axis is then time instead of distance.
Reading a Particle Picture
When a particle diagram shows tightly packed regions repeating at regular intervals, mark them as compressions. Widely spaced regions between them are rarefactions. The corresponding density graph should rise for compressions and fall for rarefactions.
Always read the axis labels. A density-versus-distance graph describes how density varies across space at one instant; a density-versus-time graph describes how density changes at one position as the wave passes.
Quiz
Which description best matches Crest?
Which description best matches Trough?
Which term matches this description: The highest point on the graphical representation, corresponding to maximum density in the representation used here.
Which term matches this description: The lowest point on the graphical representation, corresponding to minimum density.
Which statement is a key takeaway from this lesson?
Practice Problems
- On a density graph, what does a crest represent physically?
- What does a trough represent?
- Why should a sinusoidal-looking density graph not be interpreted as air particles moving vertically?
- Describe how the axes change for a density-versus-time graph.
Key Takeaways
• Sound waves can be represented graphically using variations in pressure or density. • A crest on such a graph represents a compression, while a trough represents a rarefaction. • Graphs make invisible changes in a sound wave easier to study. • The repeating pattern allows quantities such as wavelength and amplitude to be identified.