36. Longitudinal & Transverse Waves

1. Core Wave Concepts

  • Energy Transfer: Waves transfer energy from one place to another without transferring matter.

  • Oscillations: To travel, waves vibrate or oscillate.

  • Key Definitions:

    • Displacement: How far the wave has oscillated from its equilibrium (rest) point.

    • Amplitude: The maximum displacement from the equilibrium point.

    • Wavelength (λ\lambda ): The distance of one entire oscillation (e.g., from crest to crest or trough to trough).

    • Crest: The highest point of a wave.

    • Trough: The lowest point of a wave.

2. Frequency and Time Period

  • Time Period ($T$): The time it takes for one complete oscillation (measured in seconds).

  • Frequency ($f$): The number of complete oscillations per second. It is measured in Hertz (Hz).

  • Equations:

    • f=1Tf = \frac{1}{T}

    • T=1fT = \frac{1}{f}

  • Example: If the time period is 0.5s, the frequency is 1/0.5=2 Hz1 / 0.5 = 2\text{ Hz}

3. Calculating Wave Speed

The speed of a wave can be found by multiplying how long each wave is by how many waves pass per second.

Wave Speed (v)=Frequency (f)×Wavelength (λ)\text{Wave Speed } (v) = \text{Frequency } (f) \times \text{Wavelength } (\lambda)

  • Units: Speed is in m/s, Frequency is in Hz, and Wavelength must be in meters (m).

  • Example: A sound wave with a frequency of 400 Hz and a wavelength of 70 cm (0.7 m0.7\text{ m}) has a speed of 400 × 0.7 = 280m/s

4. Transverse vs. Longitudinal Waves

Type

Oscillation Direction

Examples

Transverse

Perpendicular to energy transfer (up and down).

Light, radio waves, water ripples, guitar strings.

Longitudinal

Parallel to energy transfer (back and forth).

Sound waves, seismic P-waves.

  • Longitudinal Features: These waves create regions of compression (particles squashed together) and rarefaction (particles spread out).