AP Syllabus focus: 'Sound waves are modeled as mechanical longitudinal waves. Their high-pressure and low-pressure regions are called compressions and rarefactions, respectively.'
Sound is best understood as a moving pattern of pressure change in matter. For AP Physics 2, the key model is a longitudinal mechanical wave made of alternating crowded and spread-out regions.
Sound as a Longitudinal Mechanical Wave
What the model means
A sound wave in AP Physics 2 is modeled as a disturbance traveling through a material medium.
Sound wave: A mechanical longitudinal disturbance that moves through a medium as alternating regions of higher and lower pressure.
That model emphasizes that sound is not a stream of particles traveling from the source to the listener. Instead, particles in the medium repeatedly move back and forth about an equilibrium position while the disturbance itself moves outward.
This makes sound a longitudinal wave.
Longitudinal wave: A wave in which the disturbance of the medium is parallel to the direction the wave travels.
In air, the motion of the particles is in the same forward-backward direction as the sound's propagation. A vibrating speaker cone, for example, pushes nearby air forward and then allows it to move back, starting a sequence of interactions between neighboring particles.
Compressions and Rarefactions
High-pressure and low-pressure regions
When particles in the medium are pushed closer together than usual, the local pressure becomes greater than the equilibrium pressure. That crowded region is a compression.
Compression: A region of a longitudinal sound wave where pressure is higher than equilibrium and particles are closer together than usual.
A compression is not a chunk of matter traveling permanently through the medium. It is a moving region where the medium is temporarily squeezed.
Between compressions are regions where particles are farther apart than usual and the pressure is lower than equilibrium.
A longitudinal sound wave consists of alternating high-pressure compressions and low-pressure rarefactions that move through the medium. The accompanying pressure-versus-position graph uses a sinusoidal shape to represent pressure variation in space, with crests aligned to compressions and troughs aligned to rarefactions. This helps connect particle crowding (microscopic picture) to pressure graphs (macroscopic representation). Source
These regions are called rarefactions.
Rarefaction: A region of a longitudinal sound wave where pressure is lower than equilibrium and particles are farther apart than usual.
Rarefactions are also part of the traveling pattern. As sound passes a point in the medium, that point experiences a repeating change in pressure: normal pressure, compression, normal pressure, rarefaction, and then back again.
Why these regions matter
The ideas of compression and rarefaction are central because sound in a fluid is most naturally described by pressure changes. A sound wave is therefore often discussed in terms of alternating high-pressure and low-pressure regions rather than visible peaks and troughs.
How Sound Propagates
Local motion, traveling disturbance
Compressions and rarefactions form because each particle in the medium interacts with nearby particles. If one layer of air is pushed forward, it increases the pressure on the next layer. That next layer then pushes on the following layer, so the disturbance moves through the medium.
When the source pulls back, the local pressure drops, creating a rarefaction. A continuous sound is therefore a sequence of alternating compressions and rarefactions moving away from the source.
This point is essential: the medium oscillates locally, but the pattern of pressure variation propagates. Energy is transferred by the wave, while the material itself does not flow steadily from source to detector.
In liquids and gases, this longitudinal pressure model is especially useful because the particles can bunch together and spread apart along the direction of travel. The wave is identified by these pressure and density variations, not by any permanent rearrangement of the medium.
Interpreting Diagrams of Sound
Particle diagrams and pressure graphs
A common picture of sound uses dots or short lines to represent particles of the medium.
This diagram visualizes sound propagation as alternating regions where air molecules are crowded (compressions) and spread out (rarefactions). The spacing changes move outward from the source, while individual particles only oscillate locally about equilibrium. It supports the key idea that sound is a moving pattern of pressure/density variation in a medium. Source
Where the dots are crowded together, the diagram shows a compression. Where the dots are spread apart, it shows a rarefaction.
Sound is also sometimes shown as a wave-shaped curve. For this subsubtopic, that curve must be read carefully: it often represents changing pressure or density, not particles moving up and down through space.
On a pressure-versus-position graph, high parts of the curve correspond to compressions, and low parts correspond to rarefactions. The graph is only a representation of the pattern. The actual physical disturbance remains longitudinal.
Being able to switch between these representations is important. A crowded-particle diagram and a pressure graph can describe the same sound wave in different ways.
Common Misconceptions
What to avoid
A common mistake is to think that air from the source travels all the way to the listener. In the sound-wave model, particles only undergo small back-and-forth motions around equilibrium.
Another mistake is to treat a rarefaction as an empty gap. It is not empty space. It is simply a region where the pressure is lower, and the particles are less crowded than usual.
A third mistake comes from curved graphs of sound. A sinusoidal-looking graph does not mean sound is transverse. The classification depends on the direction of particle motion relative to the wave's travel, and for sound the model is longitudinal.
FAQ
Sound depends on compressions and rarefactions in matter. In a vacuum, there are no particles to crowd together or spread apart, so no pressure disturbance can propagate.
Electromagnetic waves can cross empty space, but sound cannot because sound is a mechanical disturbance of a medium.
Not always. Solids can support both compressional motion and transverse elastic motion because their particles are more strongly connected than particles in fluids.
For AP Physics 2, ordinary sound is modeled as a longitudinal wave. If a problem is specifically about sound in air, water, or a basic pressure-wave model, use compressions and rarefactions.
Each prong moves sideways, but that sideways motion pushes and pulls on nearby air. The air in front of the prong is alternately compressed and allowed to spread out.
So the source motion may be sideways, but the sound in the air still travels as longitudinal pressure variations.
A microphone contains a thin part, often called a diaphragm, that responds to changing air pressure. Compressions push it one way, and rarefactions let it move back.
That motion is converted into an electrical signal, so the microphone turns a pressure pattern in air into a signal that can be recorded or amplified.
A clap is brief, but the air still responds by being pushed and then re-adjusting. That creates a short pressure disturbance with both high-pressure and low-pressure parts.
Instead of a long repeating pattern, the result is a short pulse that still contains the same basic longitudinal structure.
Practice Questions
(2 marks)
In a diagram of a longitudinal sound wave, region A has air particles close together. Region B has air particles farther apart than average. Identify region A and region B, and state which region has the higher pressure.
1 mark: Region A is a compression.
1 mark: Region B is a rarefaction, and region A has the higher pressure.
(5 marks)
A loudspeaker vibrates back and forth, producing sound in air. Explain why the sound is modeled as a mechanical longitudinal wave. In your answer, describe how compressions and rarefactions are produced and how the disturbance moves through the air to a listener.
1 mark: Sound is mechanical because it travels through a material medium.
1 mark: Air particles move back and forth parallel to the direction of wave travel, so the wave is longitudinal.
1 mark: Motion of the speaker in one direction pushes air particles closer together, producing a compression.
1 mark: Motion of the speaker in the opposite direction produces a rarefaction, a lower-pressure region.
1 mark: The disturbance is passed from particle to particle, so energy moves through the medium without bulk transfer of matter from source to listener.
