What's the Difference Between a Transverse and a Longitudinal Wave?

Direct Answer

In a transverse wave, particles oscillate perpendicular to the direction of wave travel. In a longitudinal wave, particles oscillate parallel to the direction of wave travel.

This distinction is part of IB Physics C.2 Wave model and applies to both SL and HL students.

The Mechanism

A travelling wave transfers energy without producing a net transfer of matter. The particles of the medium oscillate around their equilibrium positions while the disturbance moves through the medium.

For a transverse wave travelling horizontally, the particles may oscillate vertically. The displacement is therefore at right angles to the direction of energy transfer, producing crests and troughs. Waves on a stretched string are transverse, and all electromagnetic waves are transverse.

For a longitudinal wave travelling horizontally, the particles also oscillate horizontally. This produces alternating compressions, where particles are closer together, and rarefactions, where particles are farther apart. Sound travelling through air is a longitudinal wave.

Both types obey the wave equation

$$v=f\lambda$$

where $v$ is wave speed, $f$ is frequency, and $\lambda$ is wavelength. In a longitudinal wave, one wavelength can be measured from the centre of one compression to the centre of the next compression.

A common misconception is that particles travel with the wave. They do not: particles oscillate locally while energy propagates through the medium.

IB Exam Technique

For an Explain question, state both the oscillation direction and the direction of wave propagation. If interpreting a longitudinal-wave diagram, identify compressions and rarefactions rather than incorrectly calling them crests and troughs.