Waves: Properties, Characteristics, and Behaviors
Wave Mechanics
Introduction to Waves
Wave mechanics describes the collective behavior of individual particles within a medium. Waves transfer energy without transferring matter.
Types of Waves
Transverse Waves
In transverse waves, particles move perpendicular to the direction of wave propagation.
- Crest: The point of maximum positive displacement from equilibrium.
- Trough: The point of maximum negative displacement from equilibrium.
Longitudinal Waves
In longitudinal waves, particles move parallel to the direction of wave propagation.
- Compression: A region of maximum density.
- Rarefaction (Expansion): A region of minimum density.
Wave Properties
Amplitude (A)
The maximum displacement of a particle from its equilibrium position.
Wavelength (λ)
The length of one complete wave cycle. λ = V / F
Frequency (F)
The number of complete wave cycles per unit time (usually seconds). Determined by the wave source. F = 1 / T
Period (T)
The time it takes for one complete wave cycle. T = 1 / F
Speed (V)
The speed at which the wave disturbance propagates through the medium. Dependent on the medium’s properties. V = λ / T = λ x F
Wave Speed in Different Media
Wave speed depends on the medium. Sound travels faster in solids than in liquids or gases due to closer molecular proximity.
- Gases: Speed depends on pressure and temperature. Higher temperature and pressure lead to faster sound propagation.
- Solids: Speed depends on density and elasticity. Elastic materials regain their shape after deformation (e.g., steel). Inelastic materials do not (e.g., clay).
| Medium | Temperature (°C) | Speed (m/s) |
|---|---|---|
| Air | 0 | 330 |
| Air | 20 | 340 |
| Hydrogen | 0 | 1285 |
| Water | 20 | 1400 |
| Steel | 20 | 5100 |
Sound
Sound as a Wave
Sound is a longitudinal mechanical wave.
Characteristics of Sound
Pitch
Related to frequency. Higher frequency corresponds to higher pitch. Human hearing range: 20 Hz to 20,000 Hz.
Timbre
Related to the wave shape. Allows distinction between sounds of the same pitch and loudness.
Loudness (Intensity)
Related to amplitude. Measured in decibels (dB).
| Sound Level (dB) | Location/Source | Consequences |
|---|---|---|
| 130-150 | Dance clubs, jets | Adverse effects on circulatory system |
| 180 | Rocket launch | Digestive upset, attention difficulties, visual problems |
Wave Phenomena
Refraction
The change in wave speed and direction when a wave passes from one medium to another with different properties.
Reflection
The bouncing back of a wave when it reaches a boundary between two media.
Interference
The superposition of two or more waves occupying the same space. Can be constructive (increased amplitude) or destructive (decreased amplitude).
Diffraction
The bending of waves around obstacles or through openings. Most noticeable when the wavelength is comparable to the obstacle size.
Polarization
The restriction of wave oscillations to a single plane. Can be vertical or horizontal.
Doppler Effect
The apparent change in wave frequency due to relative motion between the source and observer.
Resonance
The increase in amplitude of a vibrating object when subjected to pulses at its natural frequency.