WAVES 1

• Transverse waves

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• Electric and magnetic fields oscillating perpendicular to each other

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• Do not require a medium to propagate

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• Travel at a speed of 3 x 10⁸ ms^-1 in a vacuum

Radio waves = < 10⁶

Microwaves = 10^-1

Infrared = 10^-3

Visible light = 7 x 10^-7 

Ultraviolet = 4 x 10^-7

X-rays = 10^-8 to 10^-13

Gamma rays = 10^-10 to 10^-16

• Reflected

• Refracted

• Diffracted

• Plane polarised

• Oscillation that travels through matter (or in some cases a vacuum)

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• Transfers energy from one place to another, but not matter

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• Particles in the matter vibrate, but do not move along the wave

• Particles in the medium move from their equilibrium position to a new position

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• Exert forces on each other

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• A displaced particle experiences a restoring force from its neighbours

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• Pulled back to its equilibrium position

• Medium displaced perpendicular to direction of energy transfer

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• Oscillations of medium particles perpendicular to direction of wave travel

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• Peaks and troughs

• Medium displaced in same line as direction of energy transfer

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• Oscillations of medium particles parallel to direction of wave travel

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• Compressions and rarefactions

• Distance from the equilibrium position in a particular direction 

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• A vector, so positive or negative

• Maximum displacement from the equilibrium position

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• Positive or negative

Minimum distance between two points oscillating in phase on adjacent waves

Time taken to complete one oscillation

Number of wavelengths passing a given point per unit time

Distance travelled by the wave per unit time

v (wave speed) = f (frequency) x  λ (wavelength)

f (frequency) = 1 / T (period)

• A graph showing the displacement of the particles in the wave against the distance along the wave

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• Can be used to determine the wavelength and amplitude of both types of wave

Difference between the displacements of particles along a wave/ on different waves

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0 λ = 0^o = 0π radians = in phase

0.25 λ = 90^o = 0.5π radians

0.5 λ = 180^o = 1π radians = in antiphase

0.75 λ = 270^o = 1.5π radians

1 λ = 360^o = 2π radians

In phase

• Parcticles oscillate in step with each other

• Both reach their maximum +ve displacement at the same time

• Phase difference of zero

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In antiphase

• Parcticles oscillate out of step with each other

• One reaches their maximum +ve displacement at the same time as the other reaches their maximum -ve displacement

• Phase difference of 180^o/ 1π radians

Radiant power passing through a surface per unit area

I = P / A

• I = intensity

• P = radiant power

• A = cross-sectional area

Wave travels out from source

Radiant power spreads out

Intensity is reduced

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For a point source of a wave

...energy and power spread uniformly in all directions

......over the surface of a sphere

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I = P / 4πr²

↓ intensity = ↓ ampitude as energy more spread out

......1/2 amplitude = 1/2 average speed of oscillating particles

............= 1/4 kinetic energy as E_k = ½mv²

..................= 1/4 intensity as I ∝ amplitude²

n = c / v

• n = refractive index of the material

• c = speed of light through a vacuum, 3 x 10⁸ ms^-1

• v = speed of light through the material

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↑ n = ↑ refraction towards the normal

n₁sinθ₁ = n₂sinθ₂

• θ₁ = angle between normal and incident ray

• θ₂ = angle between normal and refracted ray

• Occurs at the boundary between two different media

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• Light strikes the boundary at a large angle to the normal

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• All the light is reflected back into the original medium

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• No light energy is refracted out of the original medium

Light must be travelling through a ↑ n medium as it strikes the boundary with a ↓ n medium 

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Θ < C: refraction and partial reflection

Θ = C: refraction along the boundary between the two different media

Θ > C: total internal reflection

sinC = 1 / n

• Wave changes direction at the boundary between two different media, remaining in the original medium

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• Constant v, f and λ

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• Law of reflection: angle of incidence = angle of reflection

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• Ray shows the direction of energy transfer/ path taken by the wave

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• Wavefront is a line joining points of the wave that are in phase

• Wave changes direction as it changes speed when passing from one medium to another

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• Always partial reflection

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• Constant f

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• Wave refracts towards the normal

• ↓ λ

• Constant f

• When longitudinal waves enter a denser medium

• Wave refracts away from the normal

• ↑ λ

• Constant f

• When transverse waves enter a denser medium

• Waves passing through a gap/ around an obstacle spread out

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• Constant v, f and λ

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• ↓ gap/ obstacle = ↑ diffraction

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• Size of gap/ obstacle = wavelength of the wave = maximum diffraction

Plane polarised

• Oscillations of a transverse wave confined to a single plane

• Plane of oscillation = oscillations + direction of wave travel

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Partially polarised

• Wave reflects off a surface

• More oscillations in a particular plane

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Unpolarised

• Oscillations in many possible planes

Unpolarised light passing through a polarising filter becomes plane polarised

Rotating a second filter causes the intensity of light transmitted through to decrease

When the filters are perpendicular to each other, the intensity is zero