Graphical Representation of a Sound Wave

Introduction

Sound travels through a material medium as alternate compressions and rarefactions. In a compression, the particles of the medium are closer together, while in a rarefaction, the particles are farther apart.

To understand a sound wave clearly, we can represent it graphically. A graph helps us see how the density of the medium changes with distance when a sound wave travels through it.

Why Do We Use a Graph for Sound Waves?

Sound waves are not visible to our eyes. However, their effect on the particles of a medium can be represented by a graph.

In a sound wave, the density of the medium changes periodically. Some regions have density greater than the average density, while some regions have density less than the average density.

A graph of a sound wave helps us identify compressions, rarefactions, crests, and troughs.

Graphical Representation

A sound wave can be represented by plotting the variation of density of the medium with distance from the source at a given instant of time.

In this graph:

• The x-axis represents distance from the source.
• The y-axis represents density of the medium.
• The horizontal dashed line represents the average density of the medium.
• The regions above the average density represent compressions.
• The regions below the average density represent rarefactions.

Figure

Explanation of the Figure

The upper part of the figure shows alternate compressions and rarefactions in a medium. In compressions, particles are closer together. In rarefactions, particles are farther apart.

The lower part shows the graph of density of the medium with distance. The horizontal dashed line represents the average density of the medium.

The parts of the graph above the average density represent compressions. The parts of the graph below the average density represent rarefactions.

Compression on the Graph

In a compression, the particles of the medium are closer together. Therefore, the density of the medium becomes greater than the average density.

On the graph, compression is shown by the portion above the average density line.

Compression = Density above average density

Rarefaction on the Graph

In a rarefaction, the particles of the medium are farther apart. Therefore, the density of the medium becomes less than the average density.

On the graph, rarefaction is shown by the portion below the average density line.

Rarefaction = Density below average density

Crest

The highest point on the graphical representation of a sound wave is called the crest.

At the crest, the density of the medium is maximum. Therefore, a crest represents the region of maximum compression.

Crest = Highest point of the wave graph

Trough

The lowest point on the graphical representation of a sound wave is called the trough.

At the trough, the density of the medium is minimum. Therefore, a trough represents the region of maximum rarefaction.

Trough = Lowest point of the wave graph

Average Density

Average density is the normal density of the medium when there is no compression or rarefaction.

In the graph, average density is shown by a horizontal dashed line. The density of the medium varies above and below this line as the sound wave passes.

Periodic Variation of Density

As a sound wave propagates, the density of the medium increases and decreases repeatedly.

This repeated variation of density is called periodic variation. The graph of a sound wave shows this periodic rise and fall of density with distance.

Another Way to Represent a Sound Wave

A sound wave can also be represented by plotting the variation of density with time at a fixed point in the medium.

In that case, the x-axis represents time and the y-axis represents density of the medium.

Comparison of Regions in a Sound Wave Graph

Part of Graph	Meaning	Sound Wave Region
Above average density	Density is greater than normal	Compression
Below average density	Density is less than normal	Rarefaction
Highest point	Maximum density	Crest
Lowest point	Minimum density	Trough
Dashed horizontal line	Normal density	Average density

Why is the Graph Useful?

• It helps us understand compressions and rarefactions clearly.
• It shows how density changes with distance.
• It helps us identify crest and trough.
• It helps in studying wavelength, frequency, time period, and amplitude.
• It makes invisible sound waves easier to understand.

Examples

• When a speaker produces sound, air density changes periodically around it.
• When a tuning fork vibrates, it produces alternate compressions and rarefactions in air.
• When a drum is beaten, sound waves travel through air as periodic density variations.
• When we speak, our vocal cords produce sound waves that can be represented by density graphs.

Important Terms

1. Graphical Representation

A way of showing the variation of density of a medium with distance or time using a graph.

2. Compression

A region where the density of the medium is higher than average density.

3. Rarefaction

A region where the density of the medium is lower than average density.

4. Crest

The highest point of a wave graph representing maximum density.

5. Trough

The lowest point of a wave graph representing minimum density.

6. Average Density

The normal density of the medium when there is no sound disturbance.

Important Points

• Sound waves can be represented graphically.
• A sound wave graph commonly shows density of medium versus distance.
• Distance is plotted on the x-axis.
• Density of the medium is plotted on the y-axis.
• The horizontal dashed line represents average density.
• Compression is represented by density above the average density line.
• Rarefaction is represented by density below the average density line.
• The highest point of the graph is called the crest.
• The lowest point of the graph is called the trough.
• The graph shows periodic variation of density with distance.

Conclusion

The graphical representation of a sound wave helps us understand how the density of a medium changes during sound propagation. In this graph, distance is plotted on the x-axis and density is plotted on the y-axis. Regions above the average density represent compressions, while regions below the average density represent rarefactions. The highest point of the graph is called the crest and the lowest point is called the trough. Thus, the graph makes the invisible nature of sound waves easier to understand.