Read longitudinal compressions and rarefactions
Use local parallel vibration and complete repeated density patterns for sound, springs and seismic P-waves.
Section P3.1 · General properties of waves
Cross-referenced to the 2028–2029 0653 section using original teaching from the related single-science courses. A 0653-specific objective-by-objective and Core/Supplement review is in progress. Written practice is self-checked and does not demonstrate supervised laboratory competence or award an official Cambridge grade.
Before you begin
- Distinguish a moving pattern from material movement.
- Measure a complete spatial repeat.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
A longitudinal wave propagates right. How do its local elements vibrate?
What you will learn
- Know that longitudinal vibration is parallel to propagation.
- Identify compressions, rarefactions and the specified sound and P-wave models.
Local motion is along the propagation line
In a longitudinal wave, local vibration is parallel to the propagation direction. In a suitable spring, coils move back and forth along its axis while compressions and rarefactions propagate along it. A compression is a region where elements are closer than in the reference arrangement; a rarefaction is a more widely separated region.
A moving compression region is not the same coil population carried to every later position. The pattern passes through successive local elements. The terms describe variations relative to the medium's undisturbed state, rather than proving that a medium particle has travelled with the whole wave.
Measure matching regions and apply the examples
Wavelength is the distance from one compression centre to the next corresponding compression centre, or one rarefaction centre to the next. Compression to the next rarefaction is half a wavelength in the regular symmetric model. The width of one compressed region alone is not a complete wavelength.
Ordinary sound waves in air and seismic P-waves can be modelled as longitudinal. Sound involves local pressure/density variations and material motion, rather than air continually flowing from speaker to listener. A P-wave's local displacement is parallel to propagation; its classification differs from the transverse S-wave model. The spring and dot diagram is schematic, not a measured pressure distribution or atom-scale image.
Sources for this lesson
Pause and explain
Which distance measures longitudinal wavelength?
Worked example
A compression pattern travels right and spring coils move right and left locally. Compression centres are at 0.10 m and 0.50 m. Classify it and find wavelength.
Show the worked solution
- Local vibration is parallel to propagation.
- The model is longitudinal.
- Adjacent compression-centre separation is 0.50 − 0.10 = 0.40 m.
Answer Longitudinal; wavelength 0.40 m.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Classify a rightward compression pattern with right–left local coil motion.
Give me a hint
Compare the vibration axis and propagation axis.
Compare my reasoning
- Propagation lies along the spring.
- Coils oscillate along that same line.
- The wave is longitudinal.
Longitudinal: local vibration is parallel to propagation.
Look for these in your work
- Identify both directions.
- Distinguish oscillation from transport.
Compression centres at 0.10, 0.50 and 0.90 m form a regular wave. Find wavelength and compression-to-next-rarefaction separation.
Give me a hint
Use a complete matching repeat before halving it.
Compare my reasoning
- Adjacent compression centres are 0.40 m apart.
- Wavelength is 0.40 m.
- The symmetric compression-to-next-rarefaction separation is 0.20 m.
Wavelength 0.40 m; half-repeat separation 0.20 m.
Look for these in your work
- Use centre-to-centre intervals.
- State the symmetric-model assumption.
A student says sound reaches a listener because the same air parcel moves all the way from the speaker. Correct the account.
Give me a hint
A travelling density pattern and local material oscillation differ.
Compare my reasoning
- Air elements oscillate locally along the propagation line.
- Pressure and density variations propagate through successive interactions.
- A speaker-to-listener bulk parcel journey is not required.
Sound propagates through local longitudinal oscillations, not a compulsory bulk air stream.
Look for these in your work
- Name the local motion.
- Explain the travelling disturbance.
Common mistakes
- Compressions are moving patterns, not permanently tagged coils.
- Compression width alone is not wavelength.
- Sound does not require a bulk air stream from source to listener.
What can you explain now?
Is compression centre to next rarefaction centre a full wavelength in this regular model?
Compare with the explanation
No; half a wavelength.
A full repeat returns to the same kind and stage of the density pattern.
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Make it stick
Describe longitudinal direction, compressions, rarefactions and corresponding-centre wavelength measurements.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.