# WAVES 1

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• Created by: CPev3
• Created on: 27-05-20 21:56

## Electromagnetic waves

• 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
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## Electromagnetic spectrum

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

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## Electromagnetic waves can be...

• Reflected
• Refracted
• Diffracted
• Plane polarised
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## Progressive wave

• 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
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## Progressive wave travelling through a medium

• 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
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## Transverse (S) wave

• 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
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## Longitudinal (P) wave

• 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
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## Displacement

• Distance from the equilibrium position in a particular direction

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• A vector, so positive or negative
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## Amplitude

• Maximum displacement from the equilibrium position

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• Positive or negative
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## Wavelength

Minimum distance between two points oscillating in phase on adjacent waves

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## Period

Time taken to complete one oscillation

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## Frequency

Number of wavelengths passing a given point per unit time

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## Wave speed

Distance travelled by the wave per unit time

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## Wave equation

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

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## Frequency equation

f (frequency) = 1 / T (period)

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## Wave profile

• 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
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## Phase difference

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

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0 λ = 0o = 0π radians = in phase

0.25 λ = 90o = 0.5π radians

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

0.75 λ = 270o = 1.5π radians

1 λ = 360o = 2π radians

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## In phase/ antiphase

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 180o/ 1π radians
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## Intensity

Radiant power passing through a surface per unit area

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## Intensity equation

I = P / A

• I = intensity
• P = radiant power
• A = cross-sectional area
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## Relationship between intensity and distance

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

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## Relationship between intensity and amplitude

↓ intensity = ↓ ampitude as energy more spread out

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

............= 1/4 kinetic energy as Ek½mv2

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

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## Refractive index equation

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

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## Refraction law

n1sinθ1 = n2sinθ2

• θ1 = angle between normal and incident ray
• θ2 = angle between normal and refracted ray
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## Total internal reflection

• 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
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## Conditions for TIR

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

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sinC = 1 / n

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## Reflection

• 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
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## Refraction

• 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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## Refraction: ↑ v

• Wave refracts towards the normal
• ↓ λ
• Constant f
• When longitudinal waves enter a denser medium
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## Refraction: ↓ v

• Wave refracts away from the normal
• ↑ λ
• Constant f
• When transverse waves enter a denser medium
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## Diffraction

• 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
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## Polarisation

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
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## Polarising filters

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

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