Question

How are longitudinal and transverse waves alike? How are they different?

Answer 1

Short answer: Both types are waves that transfer energy and information through a medium or field and share common wave properties (wavelength, frequency, amplitude, speed, superposition). They differ in the direction of the medium’s (or field’s) motion relative to the wave propagation, the media they can travel in, and properties like polarization.

Similarities
- Both carry energy and usually information without a net transport of matter.
- Both are described by the same basic wave concepts and parameters: wavelength, frequency, period, amplitude, speed, phase.
- Both obey the principle of superposition and can form standing waves, show interference and diffraction (subject to geometry/scale).
- Both can be reflected and refracted at boundaries (behavior depends on impedances).

Differences
- Particle/field motion:
- Longitudinal: particles of the medium move parallel to the direction of wave propagation (compressions and rarefactions). Example: sound in air.
- Transverse: particles or field elements move perpendicular to the direction of propagation (peaks and troughs). Example: waves on a string, electromagnetic waves.
- Media required:
- Longitudinal waves can travel through solids, liquids and gases (fluids easily support compressions).
- Mechanical transverse waves require a medium that supports shear (solids, stretched strings); fluids generally cannot sustain mechanical transverse waves. (Electromagnetic transverse waves do not require a material medium.)
- Polarization:
- Transverse waves can be polarized (direction of perpendicular displacement can be chosen).
- Longitudinal waves cannot be polarized in the same way (motion is along the propagation direction).
- Wave speed dependence:
- Longitudinal wave speed in a fluid depends on bulk modulus and density (e.g., v = sqrt(B/ρ)).
- Transverse wave speed in a solid/string depends on shear modulus or tension and linear density (e.g., v = sqrt(G/ρ) or v = sqrt(T/μ) for a string).
- Typical examples:
- Longitudinal: sound waves in air, pressure waves, P-waves in earthquakes.
- Transverse: waves on a guitar string, S-waves in earthquakes (in solids), electromagnetic light waves.

That covers the main ways they are alike and differ.