Difference between transverse and longitudinal wave

The main difference between transverse and longitudinal waves in physics are presented in a simple and easy-to-read way as follows:

• In a transverse wave, the elements of the medium move perpendicular to the wave’s travel or velocity direction BUT in a longitudinal wave the elements of the medium move parallel to the direction of the wave’s velocity.
• In a transverse wave, the crests and troughs are the familiar concepts from everyday life, BUT in a longitudinal wave, compressed (high-pressure) or stretched (low-pressure) regions are produced that have the usual meaning of a crest and a trough, respectively.
• In transverse waves, the distance between two adjacent crests or troughs is called the wavelength BUT in longitudinal waves, the distance between two neighboring compressions and rarefactions is the wavelength.
• Transverse waves require a relatively rigid medium for propagation BUT longitudinal waves propagate only within the bulk of fluids and gasses.
• Energy and momentum are transferred in transverse waves by pulling on each neighboring segment of the medium BUT in longitudinal waves by pushing on adjacent segments that create low and high-density regions.
• An example of a transverse wave is a wave formed on a taut (stretched) string (standing wave) or electromagnetic wave and a longitudinal wave is a sound wave.

You can also check out the difference between electric and magnetic force. 

The difference between transverse and longitudinal waves is pictured in the following diagrams.

Setup a longitudinal wave with its waveform.

Setup a transverse wave with definitions of amplitude and wavelength.