# Compressions and rarefactions of a wave

• ravsterphysics
In summary, the displacement-time graph indicates that at point X, the displacement is zero, which means that the air molecules are not moving. This makes all three points points of rarefaction. The max displacement, either direction, is at a place with no molecules in it, which is a compression.
ravsterphysics

## The Attempt at a Solution

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Slightly confused here.

Since this is a displacement-time graph, is it correct to say that at X, since the displacement is zero that it can't be a point of compression because that would imply the air molecules are moving to and fro so they would be experiencing some displacement?

If so, then all three points would be points of rarefaction (since at rarefaction the air molecules aren't moving thus displacement = 0) so the answer would be D?

ravsterphysics said:
Since this is a displacement-time graph, is it correct to say that at X, since the displacement is zero that it can't be a point of compression because that would imply the air molecules are moving to and fro so they would be experiencing some displacement?

If so, then all three points would be points of rarefaction (since at rarefaction the air molecules aren't moving thus displacement = 0) so the answer would be D?
Rarefaction means a place where the molecules are spread out.
x is the position the molecule was, y is the current displacement from that position.
So max displacement, either direction, is at a place with no molecules in it... so is that a compression or a rarefaction?

ravsterphysics
As to your answer that displacement at X is zero, it is correct. But the displacements at Y and Z are also zero.
How can this be?
The reason is that both compressions and as well as rarefactions are corresponding to zero displacements. When you say the displacement is zero, the distance from the current position of the particle to its initial position is always considered. So it is only in compressions and rarefactions, that the said distance is zero.
Then we have to find whether the points X,Y and Z are compressions or rarefactions.
The initiating point of the graph can be considered as a point with maximum displacement. We know that the motionsum of these particles are harmonic motions.So once a particle undergoes maximum displacement, it has no option but to move back towards the centre of oscillation, that is the initial position. So when particles get closer to the centre of oscillation, the pressure will increase ( because particles are more closer to each other). An increase in pressure is a compression. So point X indicates a compression.
Once again after X, a negative peak is obtained. That peak is obtained for a negative displacement.That is a displacement towards the opposite directions. After undergoing negative displacement, the particles move further away from each other, in order to come back to the centre of oscillation. Therefore point Y should be a rarefaction because when particles move away from each other the pressure drops. Then afterwards position Z = X. So point Z is also a compression.

ravsterphysics
Put another way: consider 5 particles A B C D E F that form part of a longitudinal wave.

The table shows you each partcle, it's equilibrium position, and it's displacement at a particular instance of time:
A 0 0.9
B 1 0
C -2 0.9
D 3 0
E 4 0.9
F 5 0

so, at that time, the particles are at positions:
x = 0.9, 1, 1.1, 3, 3.9, 4, and 4.1 respectively.

Sketch those out on a number line and circle the compressions and the rarifactions.
Spot their relationship with the displacements.

ravsterphysics

## 1. What is a compression in a wave?

A compression in a wave refers to the area of high pressure or density in a wave. It occurs when the particles of the medium are pushed closely together, resulting in a region of increased pressure.

## 2. What is a rarefaction in a wave?

A rarefaction in a wave is the opposite of a compression. It is an area of low pressure or density in a wave where the particles of the medium are spread apart. This results in a decrease in pressure in that region.

## 3. How are compressions and rarefactions related in a wave?

Compressions and rarefactions are two opposite phases of a wave that occur in succession. As a wave travels through a medium, it creates areas of high pressure (compressions) and low pressure (rarefactions). These two phases are necessary for the transmission of energy through the wave.

## 4. How do compressions and rarefactions affect the amplitude of a wave?

The amplitude of a wave is the maximum displacement of a particle from its rest position. In a compression, the particles are closer together, resulting in a higher amplitude. In a rarefaction, the particles are spread apart, resulting in a lower amplitude. Therefore, compressions and rarefactions have a direct effect on the amplitude of a wave.

## 5. Can compressions and rarefactions occur in all types of waves?

Yes, compressions and rarefactions can occur in all types of waves, including mechanical waves (such as sound waves) and electromagnetic waves (such as light waves). In both cases, the particles of the medium experience areas of high and low pressure as the wave travels through them.

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