Transverse Waves

1. Definition

• Characteristics

  • Oscillation perpendicular to wave direction

  • Examples: Light waves, water waves

2. Properties

• Wavelength

  • Distance between consecutive crests or troughs

• Frequency

  • Number of oscillations per second

• Amplitude

  • Maximum displacement from rest position

• Speed

  • Determined by medium properties

3. Types

• Mechanical Waves

  • Require a medium (e.g., waves on a string)

• Electromagnetic Waves

  • Do not require a medium (e.g., radio waves, visible light)

    1. Radio waves - lowest frequency

    2. Micro waves

    3. Infrared

    4. Visible light

    5. Ultra violet

    6. X ray

    7. Gamma rays - highest frequency

4. Examples

• Water Waves

  • Surface waves on oceans and lakes

• Seismic Waves

  • S-waves during earthquakes

• Light Waves

  • Visible spectrum and beyond

5. Applications

• Communication

  • Radio and television broadcasting

• Medical Imaging

  • Ultrasound technology

• Seismology

  • Earthquake detection and analysis

6. Mathematical Representation

• Wave Equation

  • ( y(x, t) = A \sin(kx - \omega t + \phi) )

  • Where:

    • ( A ) = Amplitude

    • ( k ) = Wave number

    • ( \omega ) = Angular frequency

    • ( \phi ) = Phase constant

7. Related Concepts

• Reflection

  • Bouncing back of waves

• Refraction

  • Bending of waves when entering a different medium

• Interference

  • Superposition of waves leading to constructive or destructive interference

Longitudinal Waves

1. Definition

• Description

  • Waves where particle displacement is parallel to wave direction.

• Examples

  • Sound waves

  • Pressure waves

2. Characteristics

• Wavelength

  • Distance between successive compressions or rarefactions.

• Frequency

  • Number of waves passing a point per second.

• Amplitude

  • Maximum displacement of particles from their rest position.

3. Types

• Mechanical Waves

  • Require a medium (e.g., air, water).

• Sound Waves

  • Travel through gases, liquids, and solids.

4. Behavior

• Reflection

  • Bouncing back of waves when hitting a barrier.

• Refraction

  • Change in wave direction due to a change in medium.

• Diffraction

  • Spreading of waves when passing through an opening or around obstacles.

5. Applications

• Acoustics

  • Study of sound and its properties.

• Medical Imaging

  • Ultrasound technology.

• Seismology

  • Study of seismic waves in earthquakes.

6. Mathematical Representation

• Wave Equation

  • ( v = f \lambda ) (velocity = frequency × wavelength)

• Graphical Representation

  • Sine or cosine waves illustrating compressions and rarefactions.

7. Comparison with Transverse Waves

• Particle Motion

  • Longitudinal: Parallel to wave direction.

  • Transverse: Perpendicular to wave direction.

• Examples

  • Longitudinal: Sound waves

  • Transverse: Light waves, water waves

Equation

Speed (m/s) = Frequency (Hz) x Wavelength (m)