Transverse waves vibrate across the direction they travel
Definition
Transverse wave
A wave in which the direction of vibration is at right angles (90∘90^\circ90∘) to the direction in which the wave transfers energy.
- Shake one end of a stretched rope up and down and the wave races away horizontally while every part of the rope moves only vertically.
- Those two directions, up-and-down for the vibration and left-to-right for the energy, are perpendicular, and that is the whole definition.
- Because the material is displaced sideways, a transverse wave has a shape you can draw straight onto the page as crests and troughs.
- The sideways vibration does not have to be vertical: shaking the rope horizontally, or in a circle, still gives a transverse wave as long as the movement stays perpendicular to the travel direction.
- A stretched spring shows this too if you flick one end from side to side, sending a visible wiggle down the coils.
Longitudinal waves vibrate along the direction they travel
Definition
Longitudinal wave
A wave in which the direction of vibration is parallel to the direction in which the wave transfers energy.
- Lay a long spring on a bench, grip one end and push it forwards then pull it back along the spring's own length.
- A moving pattern of bunched-up and spread-out coils travels away from your hand, and each coil slides back and forth along the same line the wave is moving.
- The bunched-up regions are called compressions, where the material is squeezed closer together than normal.
- The stretched-out regions between them are rarefactions, where the material is spread further apart than normal.
- Compressions and rarefactions do the same job as crests and troughs, so one wavelength is the distance from one compression to the next compression.
- A longitudinal wave has no sideways displacement at all, which is why it is drawn as a row of dots rather than as a wavy line.
Key Idea
The only thing that separates the two types is the angle between the vibration and the direction of travel: 90∘90^\circ90∘ for transverse, 0∘0^\circ0∘ for longitudinal.
Real waves are modelled as one type or the other
- Three families of wave are modelled as transverse.
- All electromagnetic radiation, from radio waves through visible light to gamma rays, in which electric and magnetic fields oscillate at right angles to the direction of travel.
- Water waves, in which the surface rises and falls while the wave moves across the surface.
- Seismic S-waves (secondary waves), which shake the rock from side to side as they travel through the Earth.
- Two families are modelled as longitudinal.
- Sound waves, in which a loudspeaker cone pushes the air forwards to make a compression and pulls back to leave a rarefaction, all along the direction the sound travels.
- Seismic P-waves (primary waves), which squeeze and stretch the rock along their own path.
- The word modelled matters: real water particles actually move in small circles, but treating the wave as transverse predicts everything you need at this level.
- Everything else the two types share: both transfer energy without transferring matter, both have a wavelength, frequency, amplitude and speed, and both obey v=fλv = f\lambdav=fλ.
- One practical difference is worth knowing: longitudinal waves can travel through liquids and gases, which is why sound reaches you through air and through water.
Example
- An earthquake sends out both types at once, and the names come from the order they arrive.
- The longitudinal P-waves are faster, so a seismometer records them first as a sharp jolt.
- The transverse S-waves arrive second and shake buildings from side to side, which is what causes most of the damage.
- The gap between the two arrivals is used to work out how far away the earthquake was.
Common Mistake
- Do not describe a longitudinal wave as having crests and troughs, because it has compressions and rarefactions instead.
- Do not say sound is transverse because it is often drawn as a wavy line on a screen; that graph is a plot of pressure against time, not a picture of the air moving.
- Do not write that the particles "move along with the wave" in a longitudinal wave; they vibrate back and forth about a fixed position.
- Do not swap the seismic labels: P-waves are primary and longitudinal, S-waves are secondary and transverse.
Exam technique
- Deciding which type a diagram is showing:
- Find the arrow giving the direction of travel first, because every decision is made relative to it.
- Pick one particle, work out which way it moves, and compare that with the arrow.
- Perpendicular means transverse; along the same line means longitudinal.
- A definition here scores only if it names both directions, so write "the vibration is at right angles to the direction of travel" rather than just "it vibrates up and down".
- "Direction of travel", "direction of propagation" and "direction of energy transfer" all mean the same thing and all earn the mark.
- When you are asked for an example, give a named one from the lists above rather than a vague answer like "a wave in a solid".
- If the question asks how the two types are similar, the marks are for energy transfer without matter transfer and for sharing the same wave quantities, not for the difference.
Self review
- Define a transverse wave, referring to both directions involved.
- What are compressions and rarefactions, and which type of wave has them?
- Name three kinds of wave modelled as transverse and two modelled as longitudinal.
- Which seismic wave is longitudinal, and which arrives at a seismometer first?
- How would you measure one wavelength on a diagram of a longitudinal wave?
