The wave as a graph

The idea

At an instant, the density of the medium varies periodically with distance; on a density–distance graph the highest point (maximum density, in a compression) is the crest and the lowest (minimum density, in a rarefaction) the trough.

Density along the path

At one instant, a measuring instrument finds the density of the air at many points along the path of a sound wave, and a graph is plotted.

What do you think the graph looks like?

• A wavy line that goes above and below the average
• A straight flat line
• A line that keeps climbing

Slide along the wave

Move the point along the distance axis. Find a crest and a trough.

Highest and lowest

On the graph, the density rises above the average in a compression and falls below it in a rarefaction. The highest point is the crest and the lowest point is the trough.

At an instant, the density of the medium varies periodically with distance. On a density versus distance graph, the highest point (maximum density, in a compression) is the crest and the lowest point (minimum density, in a rarefaction) is the trough.

Notes

On a density versus distance graph, the crest is the highest point (maximum density, in a compression) and the trough is the lowest point (minimum density, in a rarefaction).

Check yourself

What does the graph of a sound wave show on its two axes?

What is the highest point of the graph called?

The lowest point of the graph is in which part of the sound wave?

What does the horizontal dashed line on the graph mark?

• Time on the x-axis and loudness on the y-axis. The graph in this section plots the distance on the x-axis and the density of the medium on the y-axis.
• Density on the x-axis and distance on the y-axis. The distance is plotted on the x-axis and the density on the y-axis.
• Distance on the x-axis and the density of the medium on the y-axis — correct. Yes!
• The crest — correct. Yes!
• The trough. The trough is the lowest point of the wave.
• The average density. The average density is marked as a horizontal dashed line, not as the highest point.
• A compression, where the density is minimum. A compression is a region of higher than average density, where the density reaches its maximum.
• A rarefaction, where the density is minimum — correct. Yes!
• A compression, where the density is maximum. The maximum density is the crest, in a compression. The lowest point is in a rarefaction.
• The crest. The crest is the highest point of the curve, not the dashed line.
• The distance from the source. The distance is plotted on the x-axis. The dashed line marks the average density.
• The average density — correct. Yes!