Transverse and longitudinal waves

Waves are disturbances that transfer energy from one place to another without transferring matter. There are two main types of mechanical waves: transverse and longitudinal.

Transverse Waves

In transverse waves, the particles of the medium vibrate perpendicular (at right angles) to the direction in which the wave travels. The classic example is a wave on a stretched string or surface water waves.

• Direction of vibration: Perpendicular to wave direction
• Examples: Light waves (electromagnetic), waves on strings, ripples on water

A transverse wave has crests (maximum displacement above the rest position) and troughs (maximum displacement below the rest position).

Longitudinal Waves

In longitudinal waves, the particles of the medium vibrate parallel to the direction in which the wave travels. The classic example is a sound wave in air.

• Direction of vibration: Parallel to wave direction
• Examples: Sound waves in air, compression waves in a spring

A longitudinal wave consists of compressions (regions where particles are close together) and rarefactions (regions where particles are spread apart).

Comparing Transverse and Longitudinal Waves

Graphical Representations

Transverse Waves

• Usually represented as a sine wave.
• The vertical axis shows displacement; the horizontal axis shows position or time.
• Key features:
  • Amplitude: Maximum displacement from the rest position.
  • Wavelength ($\lambda$): Distance between two consecutive crests or troughs.
  • Period ($T$): Time for one complete wave to pass a point.

Longitudinal Waves

• Often represented by plotting displacement or pressure against position.
• Compressions are shown as regions of high density/pressure; rarefactions as low density/pressure.
• Sometimes shown as a "wave" of alternating compressions and rarefactions along a line.

Summary Table