Waves are an important idea in physics. They help us understand how energy moves through space or other materials without changing the position of the particles in those materials.

Waves can be split into two main types:

Types of Waves

1. Transverse Waves:

   • In transverse waves, the movement of particles is at a right angle to the direction the wave travels.
   • For example, waves on a string or light waves are transverse waves.
   • We often picture transverse waves as a wavy line, like a sine wave.

2. Longitudinal Waves:

   • In longitudinal waves, the movement of particles is in the same direction as the wave travels.
   • A good example of this is sound waves, which have areas of tightness (compressions) and areas of spread-out particles (rarefactions).
   • You can think of a longitudinal wave as a series of compressions and stretches moving along.

Properties of Waves

Waves have some key properties that we can measure:

• Wavelength ($\lambda$):
  • Wavelength is the distance between two points on a wave that are in the same position, like from one crest (high point) to the next. We measure it in meters (m).
• Frequency ($f$):
  • This is how many complete waves pass by in one second. We measure frequency in hertz (Hz).
  • For example, if a wave completes 50 cycles in one second, we say its frequency is $f = 50 \, \text{Hz}$.
• Amplitude ($A$):
  • Amplitude is the biggest distance that points on the wave move from their resting position. A higher amplitude means more energy. The unit can change depending on the wave type, like meters for sound waves.

Wave Speed

The speed ($v$) of a wave depends on its type and the material it moves through. We can find wave speed using this formula:

$$v = f \cdot \lambda$$

Where:

• $v$ = wave speed (meters per second, m/s)
• $f$ = frequency (Hz)
• $\lambda$ = wavelength (meters, m)

Summary of Key Facts

• For transverse waves, energy moves at a right angle to how the particles move.
• For longitudinal waves, energy moves in the same direction as the particles.
• Typical speeds of waves are:
  • Sound waves in air: about $343 \, \text{m/s}$ at $20^\circ \text{C}$.
  • Light waves in a vacuum: about $3 \times 10^8 \, \text{m/s}$.
• Here are some frequency ranges:
  • The range of human hearing: $20 \, \text{Hz}$ to $20 \, \text{kHz}$.
  • Frequencies of visible light: $4 \times 10^{14} \, \text{Hz}$ to $8 \times 10^{14} \, \text{Hz}$.

Learning about these basic definitions and properties of waves helps us understand how they act and how they are used in different areas of physics and engineering.