#### General Waves - Types and Properties

- Waves transfer energy without transferring matter.
is the distance of a point form it undisturbed position.**Displacement**is the number of waves passing any point per second; it is the number of oscillations per unit time, measured in Hertz (Hz).**Frequency**- Frequency =
^{1}/_{Period}=^{1}/_{T}

- Frequency =
is the time taken for one complete oscillation, in seconds.**Period**is the peak of a transverse wave or the compression of a longitudinal wave.**Wavefront**is the speed at which the waveform travels in the direction of the propagation of the wave; it is how fast the wave travels, measured in**Wave Speed**^{m}/_{s}- Speed (
^{m}/_{s}) = Frequency (Hz) × Wavelength (m) - v = fλ

- Speed (
is the distance between a point on one wave to the equivalent point on the next wave, in meters.**Wavelength**is the maximum distance a wave moves from its rest position when a wave passes.**Amplitude**

- Progressive waves transfer energy from one position to another.

__Transverse and Longitudinal Waves__

__Transverse and Longitudinal Waves__

__Refraction__

__Refraction__

- Speed and wavelength is reduced but frequency stays the same and the wave changes direction.
- Waves slow down when they pass from a less dense to a more dense material and vice versa.
- When a wave is slowed down, it is refracted towards the normal (i > r)
- When a wave is sped up, it is refracted away from the normal (i < r)
- Deep water is denser than shallow water.

__Reflection__

__Reflection__

- Waves bounce away from a surface at the same angle they strike it.
- Angle of incidence = Angle of reflection
- Speed, wavelength and frequency are unchanged by reflection.

__Diffraction__

__Diffraction__

- Waves bend around the sides of obstacles or they spread out as they pass through a gap.
- Wider gaps produce less diffraction.
- When the gap size is equal to the wavelength, maximum diffraction occurs.

__Deducing Wave Equations__

__Deducing Wave Equations__

- Speed =
^{Distance}/_{Time} - Distance of 1 wavelength is λ and the time taken for this is T
- ∴ v =
^{λ}/_{T}= λ (^{1}/_{T}) - but f =
^{1}/_{T} - ∴ v = fλ

__Phase Difference__

__Phase Difference__

- Phase difference between two waves is the difference in terms of a fraction of a cycle or in terms of angles.

__Intensity__

__Intensity__

- Rate of energy transmitted per unit area is perpendicular to the direction of the wave propagation.
- Intensity ∝ (Amplitude)
^{2} - Intensity =
^{Power}/_{Cross Sectional Area}

__Polarization__

__Polarization__

- Polarization causes the vibration of particles to be confined to one direction in the plane normal to the direction of the propagation.

- Polarization can occur in transverse waves but not in longitudinal waves.

__The Doppler Effect__

__The Doppler Effect__

- The Doppler Effect arises when the source of the waves moves relative to the observer.
- It can occur in all types of waves, including sound and light.
- The Source Stationary Relative to the Observer:

- The Source Moving Towards Observer:

- The Source Moving Away from Observer:

- A change in wavelength leads to a change in frequency.
- The observed frequency (f
_{o}) is different from the actual frequency (f_{s}).- f
_{o}=^{fsv}/_{v ± vs} - where v is the speed of the wave and v
_{s}is the speed of the source relative to the observer.

- f

__Electromagnetic Waves__

__Electromagnetic Waves__

- All electromagnetic waves:
- travel at the speed of light (3 × 10
^{8}m/s) - travel in free space (do not need a medium to travel)
- can transfer energy
- are transverse waves

- travel at the speed of light (3 × 10