Question

What is common between transverse waves and longitudinal waves?

Both include an amplitude, crest, and rarefactions
Both move faster at higher temperatures
Both move slower through densely packed molecules
Both include a wavelength from compression to compression

Answer 1

None of the four choices is fully correct.

Why the choices are wrong
- "Both include an amplitude, crest, and rarefactions": amplitude applies to both, but "crest" is a transverse-wave term and "rarefaction" is a longitudinal-wave term — you won't have both on the same wave.
- "Both move faster at higher temperatures": not generally true for all waves. Sound in a gas speeds up with temperature, but transverse waves (e.g. on a string or in a solid) depend on tension and elastic moduli which do not always increase with temperature.
- "Both move slower through densely packed molecules": actually many longitudinal waves (sound) travel faster in denser solids than in gases; this statement is not generally true.
- "Both include a wavelength from compression to compression": that is the definition of wavelength for longitudinal waves; for transverse waves wavelength is crest-to-crest (or trough-to-trough).

What they do have in common
- Both have an amplitude, frequency (or period), wavelength (defined appropriately), and speed, and both transfer energy through the medium by periodic disturbance of particles about an equilibrium position.