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#### 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 ###### 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 • 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 • 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
• Phase difference between two waves is the difference in terms of a fraction of a cycle or in terms of angles. ###### 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 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.
###### Electromagnetic Waves • 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
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