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💡 Drawing sound
Plot the air’s density against distance and the invisible sound wave turns into a familiar wavy line with peaks and valleys.
What are crest and trough on a density graph?
Crest and Trough
On a density-distance graph the crest is the maximum density (compression) and the trough is the minimum density (rarefaction).
- Plot density (y-axis) against distance (x-axis) at one instant; the average density is a dashed line.
- The highest point (maximum density, a compression) is a crest .
- The lowest point (minimum density, a rarefaction) is a trough .
📚 Ready to Go Beyond
- We usually plot density against distance at one instant.
- Another way is to plot density against time .
- This is done at one fixed location in the medium.
NCERT Question 7 — Draw a graph to represent
Draw a graph to represent a sound wave for which the density amplitude is 3 units and wavelength is 4 cm.
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⏸▶ Pause and Ponder
- 6. Label compression and rarefaction by C and R on Fig. 10.17 (a) and (b), then label the axes and draw the matching curves in (c) and (d).
- Mark C wherever the dots are crowded — that is higher density.
- Mark R wherever the dots are spread out — that is lower density.
- On the graphs, label the x-axis Distance and the y-axis Density .
- Draw a horizontal dashed line for the average density .
- Every C becomes a crest above that dashed line.
- Every R becomes a trough below that dashed line.
- Wave (b) has its C and R closer together, so its curve is more squeezed.
✅ Test Yourself
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In a density–distance graph, what is a crest?
Show Answer
The highest point — the maximum density, in a compression. -
What is a trough?
Show Answer
The lowest point — the minimum density, in a rarefaction. -
What does the horizontal dashed line show?
Show Answer
The average density of the medium. -
What is plotted on the x-axis and the y-axis?
Show Answer
Distance on the x-axis, density of the medium on the y-axis.
Important Definitions
- Crest — the point of maximum density on a density-distance graph, i.e. a compression.
- Trough — the point of minimum density on a density-distance graph, i.e. a rarefaction.
