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A Level Physics

5. Waves

5.1 Progressive Waves
5.2 Description of Waves
5.3 Reflection & Refraction
5.4 Huygens' Construction
5.5 Superposition of Waves
5.6 Stationary Waves
5.7 Interference & Diffraction
5.8 Sound Waves
5.9 Doppler Effect
5.10 Electromagnetic Waves
5.11 Polarization

5.1 Progressive Waves ( examples )

Waves transfer energy, no matter transfered (EM & Mechanical).

transverse & longitudinal waves
Transverse wave - particles vibrate at 90° to direction of motion ( e.g. waves on: water, strings ).
Longitudinal wave - particles vibrate in the direction of motion ( e.g. waves in air column, sound waves ).

Progressive & Stationary waves

Progressive - disturbance spreading outwards from a source ( fundamental - energy carried ).
Stationary - 2 progressive waves travelling in opposite directions. Shape of wave does not move through medium ( stays in position - energy stored ).

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5.2 Description of Waves ( examples )

Wave profile:__wavelength ( l ), time period ( T ), phase relationship ( f ) - { between particles => time interval between particle maximums (y-axis) - as a fraction of period T. }

Wave Profile - also: transverse y (displ. 90' to x), longitudinal y (=> displ. in x direction)
displacement vs time, speed of wave v, period T, frequency f

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5.3 Reflection & Refraction ( examples )

Reflection & Refraction, Snell's law - see optics
Phase changes on reflection: wave reflected at boundary going into denser medium ( vdense < v1 ), or phase change at barrier is 1/2 a wavelength on reflection.

Phase changes on reflection

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5.4 Huygens' Construction ( examples )

- Predicts future position of a wavefront. Principle - "every point on a wavefront can be regarded as a source of secondary, spherical wavelets and the new wavefront will be the surface which touches all secondary wavelets."

Huygens' Principle Huygens' principle : reflection

Huygens' principle : refraction

Snell's Law


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5.5 Superposition of Waves ( examples )____ ( web simulation )

- When 2 waves meet they produce disturbances at the points where they overlap, this is called superposition (as a resultant vector).

____resultant of 2 waves ____Disturbances : anti-nodal - constructive interference, nodal - destructive interference

Interference - 2 periodic waves of equal frequency & amplitude meet at a point. The resultant disturbance µ phase difference.
Disturbance in phase = 2 x individual waves (constructive interference)
Disturbance out of phase (180°) = zero resultant (destructive interference)
Phase difference depends on : 1) initial phase of both waves. 2) path difference - the distances travelled by the 2 waves.

path difference

Beats - 2 waves of ' » ' equal frequency meet at a point Þ varying phase difference between them.
Beat frequency - 2 waves & superposition
Resultant frequancy, resultant is average of 2 component frequencies
Beats are variations in the amplitude from the resultant superposition (1 beat cycle => after one wave completes one more oscillation than the other).

Beat frequency, resultant is average of 2 component frequencies____f1 > f2

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5.6 Stationary Waves ( examples )

A stationary wave is produced when 2 progressive waves (= frequency, amplitude) travelling in opposite directions overlap. This can be demonstrated from the resultant of 2 wave trains passing over each other.

_______stationary waves - superposition of 2 progressive waves

Table - Stationary vs Progressive Waves

... Stationary Progressive
Wave Profile Does not move in x-direction Moves through medium at speed v
... Amplitude varies with time Constant amplitude*
Particles' Motion All particles between neighbouring node and antinode have different amplitudes All particles have the same amplitude
... All particles between neighbouring nodes move in phase All particles in one wavelength are out of phase
Energy Stored on wave as vibrations Carried through medium by wave
___________* unattenuated wave

Waves on Strings

_______waves on strings - 1st 2 modes

frequency of modes of vibration (L - 1/2 wavength, v - speed of wave, n - number of nodes/harmonics, f - frequency)

velocity of a wave on a string (T - tension, m - mass/length)

Experiment to investigate the relationship - f1 = (T/m)1/2/2L
investigating 1st harmonics using sonometer
from formula : 1st harmonic frequency w.r.t. L, T & m check relationships :_____f µ 1/L ,____f µ ÖT ,____f µ 1/Öm .

Waves in a Column of Air

harmonics in pipes/column's of air _____ actual position of displacement antinode (open end)

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5.7 Diffraction ( examples )

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5.8 Sound Waves ( examples )

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5.9 Doppler Effect ( examples )

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5.10 Electromagnetic Waves ( examples )

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5.11 Polarization ( examples )

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_ Copyright © 2005 Brendan Darrer

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Page Last Updated: November 2005