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PARTICLES AND WAVES
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PARTICLES
ParticleIndivisible: cannot give rise to simultaneous clicks of two detectorsLike a tiny ball that cannot be divided into smaller ones
PropertiesMass, velocity, momentum, energy, charge,...
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THE STANDARD MODEL
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WAVES
WaveDivisible: can give rise to simultaneous clicks in many detectorsExamples: sound waves, ocean waves, electromagnetic waves
PropertiesAmplitude, frequency, phase, length, interference
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SIMPLE HARMONIC MOTION
Time development
displacement fromequilibrium at time t
amplitudeangular frequency:2*pi* frequency= 2*pi/period
phase
(t) = A cos(!t ')
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ENERGY IN SIMPLE HARMONIC MOTION
Energy at time t
K(t) =1
2m!2A2 sin2(!t ') V(t) =
1
2m!2A2 cos2(!t ')
kinetic energy at time t potential energy at time t
kinetic and potential energyaveraged over one cycle
K= V=1
4m!2A2
Total energy at time tTime independent = conservedCan take arbitrary value
Energy averaged over one cycle
E=1
2m!2A2
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TRAVELING WAVES
Space-time development
displacement fromequilibrium of pointxat time t
amplitude
angular frequency
Wave velocityTravels one wavelength in one period
(x, t) = A sin(kx !t)
wavenumber:2*pi/wavelength
v = /T= = !/k
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WAVE EQUATION
Allowed spatiotemporal relations
@2
@t2(x, t) = v2
@2
@x2(x, t)
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WAVE REFLECTION
Reflection from hard and soft boundary
(x, t) = (x, t) + !(x, t)
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STANDING WAVES
Superposition of waves traveling in opposite directions
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STANDING WAVES
Generated by reflection from loose or fixed end
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ALMOST A STANDING WAVES
Generated by reflection at impedance discontinuity
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LONGITUDINAL SOUND WAVE
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BEATS
Superposition of waves with slightly different frequencies
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YOUNG'S DOUBLE-SLIT EXPERIMENT
Interference of waves. Young's original sketch.
Light intensitySum of all relevant waves, squared
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WAVES IN 2D
Plane wave
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WAVE VECTOR
Wave vectorAlong direction of propagationLength = wavenumberComponents = wave vectors of the corresponding waves
