General Waves - Types and Properties
- Waves transfer energy without transferring matter.
- Displacement is the distance of a point form it undisturbed position.
- Frequency is the number of waves passing any point per second; it is the number of oscillations per unit time, measured in Hertz (Hz).
- Frequency = 1/Period = 1/T
- Period is the time taken for one complete oscillation, in seconds.
- Wavefront is the peak of a transverse wave or the compression of a longitudinal wave.
- Wave Speed 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 m/s
- Speed (m/s) = Frequency (Hz) × Wavelength (m)
- v = fλ
- Wavelength is the distance between a point on one wave to the equivalent point on the next wave, in meters.
- Amplitude is the maximum distance a wave moves from its rest position when a wave passes.
- Progressive waves transfer energy from one position to another.
Transverse and Longitudinal Waves
- 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.
- 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.
- 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
- 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 between two waves is the difference in terms of a fraction of a cycle or in terms of angles.
- 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 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 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 (fo) is different from the actual frequency (fs).
- fo = fsv/v ± vs
- where v is the speed of the wave and vs is the speed of the source relative to the observer.
- All electromagnetic waves:
- travel at the speed of light (3 × 108 m/s)
- travel in free space (do not need a medium to travel)
- can transfer energy
- are transverse waves