8. Waves

Definition
Displacement: distance of a point from its undisturbed position
Amplitude: maximum displacement of particle from undisturbed position
Period: time taken for one complete oscillation
Frequency: number of oscillations per unit time
Wavelength: distance from any point on the wave to the next exactly similar point (e.g. crest to crest)
Wave speed: speed at which the waveform travels in the direction of the propagation of the wave
Progressive waves transfer energy from one position to another

Phase Difference

Phase difference between two waves is the difference in terms of fraction of a cycle or in terms of angles (A B)
Wave A leads wave B by \thetaθ or Wave B lags wave A by \thetaθ

Intensity

Rate of energy transmitted per unit area perpendicular to direction of wave propagation.

Transverse Waves
Oscillation of wave particles perpendicular to direction of propagation.
Polarization can occur
E.g. light waves
- Polarization: vibration of particles is confined in one direction in the plane normal to direction of propagation
- Longitudinal Waves
  - Oscillations of wave particle parallel to direction of propagation.
  - Polarization cannot occur
  - E.g. sound waves

Arises when source of waves moves relative to observer.
Can occur in all types of waves, including sound & light.
Source stationary relative to Observer:
- Source moving towards Observer:
- Source moving away from Observer:
- Change in wavelength leads to change in frequency
- Observed frequency (f_{0}f_o) is different from actual frequency (f_{s}f_s); related by equation:
where vv is speed of wave & v_{s}v_s is speed of source relative to observer

As electromagnetic wave progresses, wavelength decreases and frequency increases
All electromagnetic waves:
- All travel at the speed of light: 3 × 10⁸m/s
- Travel in free space (don't need medium)
- Can transfer energy
- Are transverse waves

f = \frac{